From 9b35fe42bf206dc95a65720ac222f278ab70ca9f Mon Sep 17 00:00:00 2001 From: andyeisenberg Date: Thu, 26 Feb 2026 08:49:48 -0500 Subject: [PATCH] Latest build deployed. --- _static/._009b407a9881be10.ttf | Bin 163 -> 163 bytes _static/._009b407a9881be10.ttf.gz | Bin 163 -> 163 bytes _static/._126.a976f62852f30b51.js | Bin 163 -> 163 bytes _static/._126.a976f62852f30b51.js.gz | Bin 163 -> 163 bytes _static/._126.a976f62852f30b51.js.map | Bin 163 -> 163 bytes _static/._126.a976f62852f30b51.js.map.gz | Bin 163 -> 163 bytes _static/._128.5bed857c54ac4e8b.js | Bin 163 -> 163 bytes _static/._128.5bed857c54ac4e8b.js.gz | Bin 163 -> 163 bytes _static/._128.5bed857c54ac4e8b.js.map | Bin 163 -> 163 bytes _static/._128.5bed857c54ac4e8b.js.map.gz | Bin 163 -> 163 bytes _static/._131.ee437eeefadd750d.js | Bin 163 -> 163 bytes _static/._131.ee437eeefadd750d.js.gz | Bin 163 -> 163 bytes _static/._131.ee437eeefadd750d.js.map | Bin 163 -> 163 bytes _static/._131.ee437eeefadd750d.js.map.gz | Bin 163 -> 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var(--dangerAlerts);\n}\n\n.codelens {\n margin-bottom: 20px;\n}\n\n.codecoach {\n margin-top: 20px;\n}\n\n.ac_section .alert h3:first-child {\n margin-top: 0px;\n}\n\n.activecode__stdin {\n display: block;\n width: 100%;\n resize: none;\n overflow: auto;\n margin-bottom: 20px;\n}\n\n.unittest-results__heading {\n text-align: center;\n font-weight: bold;\n font-size: 120%;\n}\n\n.unittest-results__percent {\n text-align: center;\n font-weight: bold;\n}\n\n.scratch-ac-modal {\n display: none;\n /* Hidden by default */\n position: fixed;\n /* Stay in place */\n z-index: 9000;\n /* Sit on top */\n left: calc((100% - 800px) / 2);\n width: 800px;\n top: 5%;\n max-height: 90%;\n overflow: auto;\n /* Enable scroll if needed */\n padding: 20px;\n border: 1px solid #888;\n border-radius: 10px;\n background-color: var(--background);\n}\n\n@media (max-width: 960px) {\n .scratch-ac-modal {\n width: 90%;\n left: 5%;\n }\n}\n\n.ac-modal-body,\n.ac-modal-content {\n background-color: var(--background);\n}\n\n.ac-modal-header .close {\n color: var(--bodyFont);\n}\n\n.scratch-ac-modal .close {\n position: absolute;\n top: 10px;\n right: 10px;\n cursor: pointer;\n}\n\n/* CodeTailor-related CSS START */\n.scaffolding-container {\n margin-right: 20px;\n position: fixed;\n right: 0px;\n max-height: 100%;\n overflow-y: scroll;\n top: 0px;\n padding-top: 60px;\n z-index: 999;\n}\n\n.scaffolding-container .ac_actions {\n display: none;\n}\n\n.scaffolding-container.hidden {\n display: none;\n}\n\n.parsons-scaffolding {\n border: 2px solid;\n border-color: black;\n border-radius: 10px;\n background-color: #f0f8ff;\n padding-top: 10px;\n box-shadow: 10px 5px 5px gray;\n}\n\n.scaffolding-loading-prompt.loading{\n display: block;\n}\n\n.scaffolding-loading-prompt{\n display: none;\n text-align: center;\n background-color: #ffebae;\n padding: 10px 5px;\n margin: 5px;\n font-size: 12pt;\n color: #191919;\n}\n\n.copy-button-hide {\n display: none;\n}\n\n/* open CodeTailor*/\nbutton.parsons-scaffolding-btn {\n background-color: #ED7014 !important;\n color: white !important;\n}\n\nbutton.reopen-help-btn {\n background-color: #ED7014 !important;\n color: white !important;\n}\n\n.reopen-help-btn.hide {\n display: none;\n}\n\n#loading-spinner {\n border: 4px solid #ED7014;\n border-top: 4px solid #084887;\n border-bottom: 4px solid #084887;\n border-radius: 50%;\n width: 30px;\n height: 30px;\n animation: spin 1.5s linear infinite;\n margin: 0 auto;\n}\n\n@keyframes spin {\n 0% { transform: rotate(0deg); }\n 100% { transform: rotate(360deg); }\n}\n/* CodeTailor-related CSS END */","/* BASICS */\n\n.CodeMirror {\n /* Set height, width, borders, and global font properties here */\n font-family: monospace;\n height: 300px;\n color: black;\n direction: ltr;\n}\n\n/* PADDING */\n\n.CodeMirror-lines {\n padding: 4px 0; /* Vertical padding around content */\n}\n.CodeMirror pre.CodeMirror-line,\n.CodeMirror pre.CodeMirror-line-like {\n padding: 0 4px; /* Horizontal padding of content */\n}\n\n.CodeMirror-scrollbar-filler, .CodeMirror-gutter-filler {\n background-color: white; /* The little square between H and V scrollbars */\n}\n\n/* GUTTER */\n\n.CodeMirror-gutters {\n border-right: 1px solid #ddd;\n background-color: #f7f7f7;\n white-space: nowrap;\n}\n.CodeMirror-linenumbers {}\n.CodeMirror-linenumber {\n padding: 0 3px 0 5px;\n min-width: 20px;\n text-align: right;\n color: #999;\n white-space: nowrap;\n}\n\n.CodeMirror-guttermarker { color: black; }\n.CodeMirror-guttermarker-subtle { color: #999; }\n\n/* CURSOR */\n\n.CodeMirror-cursor {\n border-left: 1px solid black;\n border-right: none;\n width: 0;\n}\n/* Shown when moving in bi-directional text */\n.CodeMirror div.CodeMirror-secondarycursor {\n border-left: 1px solid silver;\n}\n.cm-fat-cursor .CodeMirror-cursor {\n width: auto;\n border: 0 !important;\n background: #7e7;\n}\n.cm-fat-cursor div.CodeMirror-cursors {\n z-index: 1;\n}\n.cm-fat-cursor .CodeMirror-line::selection,\n.cm-fat-cursor .CodeMirror-line > span::selection, \n.cm-fat-cursor .CodeMirror-line > span > span::selection { background: transparent; }\n.cm-fat-cursor .CodeMirror-line::-moz-selection,\n.cm-fat-cursor .CodeMirror-line > span::-moz-selection,\n.cm-fat-cursor .CodeMirror-line > span > span::-moz-selection { background: transparent; }\n.cm-fat-cursor { caret-color: transparent; }\n@-moz-keyframes blink {\n 0% {}\n 50% { background-color: transparent; }\n 100% {}\n}\n@-webkit-keyframes blink {\n 0% {}\n 50% { background-color: transparent; }\n 100% {}\n}\n@keyframes blink {\n 0% {}\n 50% { background-color: transparent; }\n 100% {}\n}\n\n/* Can style cursor different in overwrite (non-insert) mode */\n.CodeMirror-overwrite .CodeMirror-cursor {}\n\n.cm-tab { display: inline-block; text-decoration: inherit; }\n\n.CodeMirror-rulers {\n position: absolute;\n left: 0; right: 0; top: -50px; bottom: 0;\n overflow: hidden;\n}\n.CodeMirror-ruler {\n border-left: 1px solid #ccc;\n top: 0; bottom: 0;\n position: absolute;\n}\n\n/* DEFAULT THEME */\n\n.cm-s-default .cm-header {color: blue;}\n.cm-s-default .cm-quote {color: #090;}\n.cm-negative {color: #d44;}\n.cm-positive {color: #292;}\n.cm-header, .cm-strong {font-weight: bold;}\n.cm-em {font-style: italic;}\n.cm-link {text-decoration: underline;}\n.cm-strikethrough {text-decoration: line-through;}\n\n.cm-s-default .cm-keyword {color: #708;}\n.cm-s-default .cm-atom {color: #219;}\n.cm-s-default .cm-number {color: #164;}\n.cm-s-default .cm-def {color: #00f;}\n.cm-s-default .cm-variable,\n.cm-s-default .cm-punctuation,\n.cm-s-default .cm-property,\n.cm-s-default .cm-operator {}\n.cm-s-default .cm-variable-2 {color: #05a;}\n.cm-s-default .cm-variable-3, .cm-s-default .cm-type {color: #085;}\n.cm-s-default .cm-comment {color: #a50;}\n.cm-s-default .cm-string {color: #a11;}\n.cm-s-default .cm-string-2 {color: #f50;}\n.cm-s-default .cm-meta {color: #555;}\n.cm-s-default .cm-qualifier {color: #555;}\n.cm-s-default .cm-builtin {color: #30a;}\n.cm-s-default .cm-bracket {color: #997;}\n.cm-s-default .cm-tag {color: #170;}\n.cm-s-default .cm-attribute {color: #00c;}\n.cm-s-default .cm-hr {color: #999;}\n.cm-s-default .cm-link {color: #00c;}\n\n.cm-s-default .cm-error {color: #f00;}\n.cm-invalidchar {color: #f00;}\n\n.CodeMirror-composing { border-bottom: 2px solid; }\n\n/* Default styles for common addons */\n\ndiv.CodeMirror span.CodeMirror-matchingbracket {color: #0b0;}\ndiv.CodeMirror span.CodeMirror-nonmatchingbracket {color: #a22;}\n.CodeMirror-matchingtag { background: rgba(255, 150, 0, .3); }\n.CodeMirror-activeline-background {background: #e8f2ff;}\n\n/* STOP */\n\n/* The rest of this file contains styles related to the mechanics of\n the editor. You probably shouldn't touch them. */\n\n.CodeMirror {\n position: relative;\n overflow: hidden;\n background: white;\n}\n\n.CodeMirror-scroll {\n overflow: scroll !important; /* Things will break if this is overridden */\n /* 50px is the magic margin used to hide the element's real scrollbars */\n /* See overflow: hidden in .CodeMirror */\n margin-bottom: -50px; margin-right: -50px;\n padding-bottom: 50px;\n height: 100%;\n outline: none; /* Prevent dragging from highlighting the element */\n position: relative;\n z-index: 0;\n}\n.CodeMirror-sizer {\n position: relative;\n border-right: 50px solid transparent;\n}\n\n/* The fake, visible scrollbars. Used to force redraw during scrolling\n before actual scrolling happens, thus preventing shaking and\n flickering artifacts. */\n.CodeMirror-vscrollbar, .CodeMirror-hscrollbar, .CodeMirror-scrollbar-filler, .CodeMirror-gutter-filler {\n position: absolute;\n z-index: 6;\n display: none;\n outline: none;\n}\n.CodeMirror-vscrollbar {\n right: 0; top: 0;\n overflow-x: hidden;\n overflow-y: scroll;\n}\n.CodeMirror-hscrollbar {\n bottom: 0; left: 0;\n overflow-y: hidden;\n overflow-x: scroll;\n}\n.CodeMirror-scrollbar-filler {\n right: 0; bottom: 0;\n}\n.CodeMirror-gutter-filler {\n left: 0; bottom: 0;\n}\n\n.CodeMirror-gutters {\n position: absolute; left: 0; top: 0;\n min-height: 100%;\n z-index: 3;\n}\n.CodeMirror-gutter {\n white-space: normal;\n height: 100%;\n display: inline-block;\n vertical-align: top;\n margin-bottom: -50px;\n}\n.CodeMirror-gutter-wrapper {\n position: absolute;\n z-index: 4;\n background: none !important;\n border: none !important;\n}\n.CodeMirror-gutter-background {\n position: absolute;\n top: 0; bottom: 0;\n z-index: 4;\n}\n.CodeMirror-gutter-elt {\n position: absolute;\n cursor: default;\n z-index: 4;\n}\n.CodeMirror-gutter-wrapper ::selection { background-color: transparent }\n.CodeMirror-gutter-wrapper ::-moz-selection { background-color: transparent }\n\n.CodeMirror-lines {\n cursor: text;\n min-height: 1px; /* prevents collapsing before first draw */\n}\n.CodeMirror pre.CodeMirror-line,\n.CodeMirror pre.CodeMirror-line-like {\n /* Reset some styles that the rest of the page might have set */\n -moz-border-radius: 0; -webkit-border-radius: 0; border-radius: 0;\n border-width: 0;\n background: transparent;\n font-family: inherit;\n font-size: inherit;\n margin: 0;\n white-space: pre;\n word-wrap: normal;\n line-height: inherit;\n color: inherit;\n z-index: 2;\n position: relative;\n overflow: visible;\n -webkit-tap-highlight-color: transparent;\n -webkit-font-variant-ligatures: contextual;\n font-variant-ligatures: contextual;\n}\n.CodeMirror-wrap pre.CodeMirror-line,\n.CodeMirror-wrap pre.CodeMirror-line-like {\n word-wrap: break-word;\n white-space: pre-wrap;\n word-break: normal;\n}\n\n.CodeMirror-linebackground {\n position: absolute;\n left: 0; right: 0; top: 0; bottom: 0;\n z-index: 0;\n}\n\n.CodeMirror-linewidget {\n position: relative;\n z-index: 2;\n padding: 0.1px; /* Force widget margins to stay inside of the container */\n}\n\n.CodeMirror-widget {}\n\n.CodeMirror-rtl pre { direction: rtl; }\n\n.CodeMirror-code {\n outline: none;\n}\n\n/* Force content-box sizing for the elements where we expect it */\n.CodeMirror-scroll,\n.CodeMirror-sizer,\n.CodeMirror-gutter,\n.CodeMirror-gutters,\n.CodeMirror-linenumber {\n -moz-box-sizing: content-box;\n box-sizing: content-box;\n}\n\n.CodeMirror-measure {\n position: absolute;\n width: 100%;\n height: 0;\n overflow: hidden;\n visibility: hidden;\n}\n\n.CodeMirror-cursor {\n position: absolute;\n pointer-events: none;\n}\n.CodeMirror-measure pre { position: static; }\n\ndiv.CodeMirror-cursors {\n visibility: hidden;\n position: relative;\n z-index: 3;\n}\ndiv.CodeMirror-dragcursors {\n visibility: visible;\n}\n\n.CodeMirror-focused div.CodeMirror-cursors {\n visibility: visible;\n}\n\n.CodeMirror-selected { background: #d9d9d9; }\n.CodeMirror-focused .CodeMirror-selected { background: #d7d4f0; }\n.CodeMirror-crosshair { cursor: crosshair; }\n.CodeMirror-line::selection, .CodeMirror-line > span::selection, .CodeMirror-line > span > span::selection { background: #d7d4f0; }\n.CodeMirror-line::-moz-selection, .CodeMirror-line > span::-moz-selection, .CodeMirror-line > span > span::-moz-selection { background: #d7d4f0; }\n\n.cm-searching {\n background-color: #ffa;\n background-color: rgba(255, 255, 0, .4);\n}\n\n/* Used to force a border model for a node */\n.cm-force-border { padding-right: .1px; }\n\n@media print {\n /* Hide the cursor when printing */\n .CodeMirror div.CodeMirror-cursors {\n visibility: hidden;\n }\n}\n\n/* See issue #2901 */\n.cm-tab-wrap-hack:after { content: ''; }\n\n/* Help users use markselection to safely style text background */\nspan.CodeMirror-selectedtext { background: none; }\n","\n.CodeMirror {\n font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;\n}\n\n// Force some colors to match those used by PreTeXt for syntax highlighting\n.cm-s-default .cm-comment { color: #3a812e; }\n.cm-s-default .cm-keyword { color: #0679B7; }\n.cm-s-default .cm-variable { color: #5e1ca0; }\n\n// Values pulled from codemirror/theme/blackboard.css\n:root.dark-mode {\n .ptx-runestone-container,.runestone-sphinx {\n .cm-s-default.CodeMirror { background: #141414; color: #F8F8F8; }\n .cm-s-default div.CodeMirror-selected { background: #364f95; }\n .cm-s-default .CodeMirror-line::selection, .cm-s-default .CodeMirror-line > span::selection, .cm-s-default .CodeMirror-line > span > span::selection { background: rgba(37, 59, 118, .99); }\n .cm-s-default .CodeMirror-line::-moz-selection, .cm-s-default .CodeMirror-line > span::-moz-selection, .cm-s-default .CodeMirror-line > span > span::-moz-selection { background: rgba(37, 59, 118, .99); }\n .cm-s-default .CodeMirror-gutters { background: #0C1021; border-right: 0; }\n .cm-s-default .CodeMirror-guttermarker { color: #FBDE2D; }\n .cm-s-default .CodeMirror-guttermarker-subtle { color: #888; }\n .cm-s-default .CodeMirror-linenumber { color: #888; }\n .cm-s-default .CodeMirror-cursor { border-left: 1px solid #A7A7A7; }\n\n .cm-s-default .cm-keyword { color: #2d94fb; }\n .cm-s-default .cm-atom { color: #abc792; }\n .cm-s-default .cm-number { color: #abc792; }\n .cm-s-default .cm-def { color: #8DA6CE; }\n .cm-s-default .cm-variable { color: #e3e1c2; }\n .cm-s-default .cm-operator { color: #F8F8F8; }\n .cm-s-default .cm-comment { color: #68a950; }\n .cm-s-default .cm-string { color: #ca9147; }\n .cm-s-default .cm-string-2 { color: #ca9147; }\n .cm-s-default .cm-meta { color: #D8FA3C; }\n .cm-s-default .cm-builtin { color: #2d94fb; }\n .cm-s-default .cm-tag { color: #8DA6CE; }\n .cm-s-default .cm-attribute { color: #8DA6CE; }\n .cm-s-default .cm-header { color: #cad18a; }\n .cm-s-default .cm-hr { color: #AEAEAE; }\n .cm-s-default .cm-link { color: #8DA6CE; }\n .cm-s-default .cm-error { background: #9D1E15; color: #F8F8F8; }\n\n .cm-s-default .CodeMirror-activeline-background { background: #3C3636; }\n .cm-s-default .CodeMirror-matchingbracket { outline:1px solid grey;color:white !important; }\n\n [lang=\"cpp\"] {\n .cm-s-default .cm-type { color: rgb(45, 148, 251); }\n }\n }\n .CodeMirror__gutter-locked-marker {\n background-color: #888;\n }\n}",".CodeMirror-hints {\n position: absolute;\n z-index: 10;\n overflow: hidden;\n list-style: none;\n\n margin: 0;\n padding: 2px;\n\n -webkit-box-shadow: 2px 3px 5px rgba(0,0,0,.2);\n -moz-box-shadow: 2px 3px 5px rgba(0,0,0,.2);\n box-shadow: 2px 3px 5px rgba(0,0,0,.2);\n border-radius: 3px;\n border: 1px solid silver;\n\n 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>TLIQ`I>px#p4NlbD00IC2fjB{U diff --git a/_static/webpack_static_imports.xml b/_static/webpack_static_imports.xml index e203fa4..d373cf7 100755 --- a/_static/webpack_static_imports.xml +++ b/_static/webpack_static_imports.xml @@ -1,7 +1,7 @@ - prefix-runtime.d892923478694492.bundle.js + prefix-runtime.529fd9398bfbd03e.bundle.js prefix-723.3e6434f80549315a.bundle.js prefix-runestone.1d6e4aba17c2c7f2.bundle.js @@ -10,5 +10,5 @@ prefix-runestone.6ec5960970d8b364.css https://runestone.academy/cdn/runestone/ - 7.11.14 + 7.11.15 diff --git a/app-Phi-table.html b/app-Phi-table.html index 0cceeb9..d1e5c51 100755 --- a/app-Phi-table.html +++ b/app-Phi-table.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/backmatter-2.html b/backmatter-2.html index 17a5d93..97caf1c 100755 --- a/backmatter-2.html +++ b/backmatter-2.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/backmatter-3.html b/backmatter-3.html index f82a8d3..db4afc3 100755 --- a/backmatter-3.html +++ b/backmatter-3.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/backmatter.html b/backmatter.html index 7ca1ef0..bc00e1e 100755 --- a/backmatter.html +++ b/backmatter.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/ch-Confidence-Intervals.html b/ch-Confidence-Intervals.html index ff0fc85..975b862 100755 --- a/ch-Confidence-Intervals.html +++ b/ch-Confidence-Intervals.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/ch-Expected-Value.html b/ch-Expected-Value.html index 0dfb3df..6b67e2b 100755 --- a/ch-Expected-Value.html +++ b/ch-Expected-Value.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/ch-Hypothesis-Testing.html b/ch-Hypothesis-Testing.html index 7b003e2..0322769 100755 --- a/ch-Hypothesis-Testing.html +++ b/ch-Hypothesis-Testing.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/ch-Introduction.html b/ch-Introduction.html index dbd188c..a164bf1 100755 --- a/ch-Introduction.html +++ b/ch-Introduction.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/ch-Linear-Regression.html b/ch-Linear-Regression.html index 61efa52..8960a40 100755 --- a/ch-Linear-Regression.html +++ b/ch-Linear-Regression.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/ch-Probability.html b/ch-Probability.html index 631671e..1e94ca2 100755 --- a/ch-Probability.html +++ b/ch-Probability.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/ch-Random-Variables.html b/ch-Random-Variables.html index f7c0e21..55dbac7 100755 --- a/ch-Random-Variables.html +++ b/ch-Random-Variables.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/front-colophon.html b/front-colophon.html index 2a28f97..5792984 100755 --- a/front-colophon.html +++ b/front-colophon.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/frontmatter.html b/frontmatter.html index 2bc0290..6827efd 100755 --- a/frontmatter.html +++ b/frontmatter.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -311,7 +311,7 @@ eBookConfig.enable_chatcodes = false;

Andy Eisenberg
Mathematics Department
Temple University
-
February 19, 2026
+
February 26, 2026
πŸ”—
PrevTopNext diff --git a/index.html b/index.html index 6a209d0..a88ee0c 100755 --- a/index.html +++ b/index.html @@ -2,7 +2,7 @@ - + diff --git a/knowl/xref/example-binomial-variance.html b/knowl/xref/example-binomial-variance.html new file mode 100755 index 0000000..682c016 --- /dev/null +++ b/knowl/xref/example-binomial-variance.html @@ -0,0 +1,39 @@ + + + + + + + + + + + + + + + + + + + + +

+Example 3.2.7. +

+
+
Recall the setup from ExampleΒ 3.1.11: a binomial random variable \(S\) is the sum \(H_1 + H_2 + \dotsb + H_n\) of \(n\) indicator random variables, each with parameter \(p\text{.}\) The results of different coin flips are independent from each other, so the random variables \(H_1, \dotsc, H_n\) are independent from each other. From ExampleΒ 3.2.6, we know that \(\Var(H_i) = p(1-p)\) for each \(i\text{.}\) Therefore:
+
+\begin{align*} +\Var(S) \amp = \Var(H_1 + H_2 + \dotsb + H_n) \\ +\amp = \Var(H_1) + \Var(H_2) + \dotsb + \Var(H_n) \\ +\amp = \underbrace{p(1-p) + p(1-p) + \dotsb + p(1-p)}_{n \text{ times}} \\ +\amp = np(1-p). +\end{align*} +
+
Remember this formula! We’ll make frequent use of it.
+
πŸ”—
+
+
πŸ”—
in-context + + diff --git a/lunr-pretext-search-index.js b/lunr-pretext-search-index.js index 41393d6..d99f9e1 100755 --- a/lunr-pretext-search-index.js +++ b/lunr-pretext-search-index.js @@ -1438,7 +1438,52 @@ var ptx_lunr_docs = [ "type": "Section", "number": "4.3", "title": "Confidence Intervals", - "body": " Confidence Intervals Text of section. Suppose we flip a coin 100 times and count 60 heads. Let be the (unknown) probability that the coin comes up heads on a flip. Give an approximate 95% confidence interval for the value of . Suppose in a sample of 100 people, 12 are left-handed. Give a 95% confidence interval for the proportion of left-handed people. Give a 90% confidence interval. The weights of five mice are measured and recorded below. Give a 95% confidence interval for the sample mean weight of mice. (Pretend 5 measurements is large enough for the CLT to apply.) mouse 1 2 3 4 5 weight (g) 26 32 33 20 29 The heights of five plants are measured and recorded below. Give a 95% confidence interval around the sample mean for the heights of the plants. (Pretend 5 measurements is large enough for the CLT to apply.) plant 1 2 3 4 5 height (in) 15 14 18 21 17 " + "body": " Confidence Intervals When estimating the value of some parameter, the maximum likelihood estimation provides the single estimate with highest possible likelihood. But we might prefer to have a range of values, with some quantitative measure of how certain we are that the true parameter value could be in the range. Suppose some measurement has a mean and variance across the entire population. Independent measurements and calculate the sample mean Then, according to , as long as we take a sufficient number of measurements. However, we don't have access to the true values of . We can make an estimate of from the collected data, so we know how spread out the normal distribution should be. Let be independent samples taken from a population. Let be the sample mean. The sample variance is: The expression: is called the standard error of the mean . Note that is an estimate of the variance of each individual measurement taken from the population. Therefore, is an estimate of the variance of the mean . Hence \"standard error of the mean\" is an estimate of the standard deviation of the mean. Next, we want to pick a distance so that our measured sample mean is within of the true population mean with a high probability. We can pick some value , and let . Then the interval: is called a confidence interval with confidence level . Let be independent samples taken from a population. Suppose is the sample mean and the sample variance. Then the 95% confidence limits are: Suppose measurements are taken of the heights of several plants in a garden plot. The measurements are given below. (Note: for the sake of a managable calculation, only five measurements are given. However, for to apply, the number of measurements would need to be greater.) Plant Height Measurements Plant Height (in) Then the sample mean is: The sum of the squares is: So the sample variance is: Now, the standard error of the mean is: Finally, we can give 95% confidence limits: If the individual measurements are indicator random variables, then the mean represents the proportion which take on the value 1. For example, if the 's indicate heads on coin flips, then represents the proportion which come up heads. In this setting, we have a nice shortcut formula ( ) for the variance of . We can make use of this formula to get the variance of without going through the sample variance calculation above: Since we won't have access to the true value of , we can use the maximum likelihood estimate . Suppose in a sample of 100 people, 40 have a particular trait. The maximum likelihood estimate for the probability of a random person having the trait is . So the standard error will be: Therefore, 95% confidence limits for are: Suppose we flip a coin 100 times and count 60 heads. Let be the (unknown) probability that the coin comes up heads on a flip. Give an approximate 95% confidence interval for the value of . . Suppose in a sample of 100 people, 12 are left-handed. Give a 95% confidence interval for the proportion of left-handed people. . Give a 90% confidence interval. . The weights of five mice are measured and recorded below. Give a 95% confidence interval for the sample mean weight of mice. (Pretend 5 measurements is large enough for the CLT to apply.) mouse weight (g) 1 26 2 32 3 33 4 20 5 29 . The heights of five plants are measured and recorded below. Give a 95% confidence interval around the sample mean for the heights of the plants. (Pretend 5 measurements is large enough for the CLT to apply.) plant height (in) 1 15 2 14 3 18 4 21 5 17 . " +}, +{ + "id": "def-sample-variance", + "level": "2", + "url": "sec-Confidence-Intervals.html#def-sample-variance", + "type": "Definition", + "number": "4.3.1", + "title": "", + "body": " Let be independent samples taken from a population. Let be the sample mean. The sample variance is: The expression: is called the standard error of the mean . " +}, +{ + "id": "sec-Confidence-Intervals-7", + "level": "2", + "url": "sec-Confidence-Intervals.html#sec-Confidence-Intervals-7", + "type": "Paragraph (with a defined term)", + "number": "", + "title": "", + "body": "confidence interval " +}, +{ + "id": "thm-CI", + "level": "2", + "url": "sec-Confidence-Intervals.html#thm-CI", + "type": "Theorem", + "number": "4.3.2", + "title": "", + "body": " Let be independent samples taken from a population. Suppose is the sample mean and the sample variance. Then the 95% confidence limits are: " +}, +{ + "id": "sec-Confidence-Intervals-9", + "level": "2", + "url": "sec-Confidence-Intervals.html#sec-Confidence-Intervals-9", + "type": "Example", + "number": "4.3.3", + "title": "", + "body": " Suppose measurements are taken of the heights of several plants in a garden plot. The measurements are given below. (Note: for the sake of a managable calculation, only five measurements are given. However, for to apply, the number of measurements would need to be greater.) Plant Height Measurements Plant Height (in) Then the sample mean is: The sum of the squares is: So the sample variance is: Now, the standard error of the mean is: Finally, we can give 95% confidence limits: " +}, +{ + "id": "sec-Confidence-Intervals-11", + "level": "2", + "url": "sec-Confidence-Intervals.html#sec-Confidence-Intervals-11", + "type": "Example", + "number": "4.3.5", + "title": "", + "body": " Suppose in a sample of 100 people, 40 have a particular trait. The maximum likelihood estimate for the probability of a random person having the trait is . So the standard error will be: Therefore, 95% confidence limits for are: " }, { "id": "exercises-Confidence-Intervals-1", @@ -1447,7 +1492,7 @@ var ptx_lunr_docs = [ "type": "Exercise", "number": "4.3.1", "title": "", - "body": " Suppose we flip a coin 100 times and count 60 heads. Let be the (unknown) probability that the coin comes up heads on a flip. Give an approximate 95% confidence interval for the value of . " + "body": " Suppose we flip a coin 100 times and count 60 heads. Let be the (unknown) probability that the coin comes up heads on a flip. Give an approximate 95% confidence interval for the value of . . " }, { "id": "exercises-Confidence-Intervals-2", @@ -1456,7 +1501,7 @@ var ptx_lunr_docs = [ "type": "Exercise", "number": "4.3.2", "title": "", - "body": " Suppose in a sample of 100 people, 12 are left-handed. Give a 95% confidence interval for the proportion of left-handed people. Give a 90% confidence interval. " + "body": " Suppose in a sample of 100 people, 12 are left-handed. Give a 95% confidence interval for the proportion of left-handed people. . Give a 90% confidence interval. . " }, { "id": "exercises-Confidence-Intervals-3", @@ -1465,7 +1510,7 @@ var ptx_lunr_docs = [ "type": "Exercise", "number": "4.3.3", "title": "", - "body": " The weights of five mice are measured and recorded below. Give a 95% confidence interval for the sample mean weight of mice. (Pretend 5 measurements is large enough for the CLT to apply.) mouse 1 2 3 4 5 weight (g) 26 32 33 20 29 " + "body": " The weights of five mice are measured and recorded below. Give a 95% confidence interval for the sample mean weight of mice. (Pretend 5 measurements is large enough for the CLT to apply.) mouse weight (g) 1 26 2 32 3 33 4 20 5 29 . " }, { "id": "exercises-Confidence-Intervals-4", @@ -1474,7 +1519,7 @@ var ptx_lunr_docs = [ "type": "Exercise", "number": "4.3.4", "title": "", - "body": " The heights of five plants are measured and recorded below. Give a 95% confidence interval around the sample mean for the heights of the plants. (Pretend 5 measurements is large enough for the CLT to apply.) plant 1 2 3 4 5 height (in) 15 14 18 21 17 " + "body": " The heights of five plants are measured and recorded below. Give a 95% confidence interval around the sample mean for the heights of the plants. (Pretend 5 measurements is large enough for the CLT to apply.) plant height (in) 1 15 2 14 3 18 4 21 5 17 . " }, { "id": "sec-One-Sample-Tests", diff --git a/my-great-book.html b/my-great-book.html index 5059f7c..74481ee 100755 --- a/my-great-book.html +++ b/my-great-book.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-CLT.html b/sec-CLT.html index c5b1f72..feef258 100755 --- a/sec-CLT.html +++ b/sec-CLT.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -463,7 +463,7 @@ Z \amp = \frac{S_{100} - 50}{\sqrt{25}} \\
Answer.
-\(\Pr(3.45 \leq m \leq 3.55) \approx 0.6141 - 0.3859 = 0.2282.\)
πŸ”—
+\(\Pr(3.45 \leq m \leq 3.55) \approx 0.6255 - 0.3745 = 0.2510.\)
πŸ”—
πŸ”—
diff --git a/sec-Chi-Squared.html b/sec-Chi-Squared.html index 86ae044..6993af7 100755 --- a/sec-Chi-Squared.html +++ b/sec-Chi-Squared.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-Conditional-Probability.html b/sec-Conditional-Probability.html index 7b1cb1e..4ffa86f 100755 --- a/sec-Conditional-Probability.html +++ b/sec-Conditional-Probability.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-Confidence-Intervals.html b/sec-Confidence-Intervals.html index 92506a9..5d96d4b 100755 --- a/sec-Confidence-Intervals.html +++ b/sec-Confidence-Intervals.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + @@ -309,64 +309,264 @@ eBookConfig.enable_chatcodes = false;

Section 4.3 Confidence Intervals

-
Text of section.
πŸ”—
+
When estimating the value of some parameter, the maximum likelihood estimation provides the single estimate with highest possible likelihood. But we might prefer to have a range of values, with some quantitative measure of how certain we are that the true parameter value could be in the range.
πŸ”—
-

+
+
Suppose some measurement has a mean \(\mu\) and variance \(\sigma^2\) across the entire population. Independent measurements \(X_1, X_2, \dotsc, X_n\) and calculate the sample mean
+
+\begin{gather*} +A_n = \frac{X_1 + \dotsb + X_n}{n}. +\end{gather*} +
+
Then, according to TheoremΒ 4.2.1, \(A_n \approx \Norm\left(\mu, \frac{\sigma^2}{n}\right)\) as long as we take a sufficient number of measurements. However, we don’t have access to the true values of \(\mu, \sigma^2\text{.}\) +
+
πŸ”—
+
+
We can make an estimate \(s^2\) of \(\sigma^2\) from the collected data, so we know how spread out the normal distribution should be.
πŸ”—
+
+

+Definition 4.3.1. +

+
+
Let \(X_1, X_2, \dotsc, X_n\) be independent samples taken from a population. Let \(A_n = \frac{X_1 + \dotsb + X_n}{n}\) be the sample mean. The sample variance is:
+
+\begin{gather*} +s^2 = \frac{\sum \left(X_i - A_n\right)^2}{n - 1} = \frac{\left(\sum X_i^2\right) - n \left(A_n\right)^2}{n - 1}. +\end{gather*} +
+
The expression:
+
+\begin{gather*} +\sqrt{\frac{s^2}{n}} = \frac{s}{\sqrt{n}} +\end{gather*} +
+
is called the standard error of the mean.
+
πŸ”—
+
+
πŸ”—
Note that \(s^2\) is an estimate of the variance of each individual measurement \(X_i\) taken from the population. Therefore, \(\frac{s^2}{n}\) is an estimate of the variance of the mean \(A_n\text{.}\) Hence "standard error of the mean" is an estimate of the standard deviation of the mean.
πŸ”—
+
+
+
Next, we want to pick a distance \(c\) so that our measured sample mean \(A_n\) is within \(c\) of the true population mean \(\mu\) with a high probability. We can pick some value \(\alpha \in (0, 1)\text{,}\) and let \(c_{\alpha} = \Phi^{-1}\left(1 - \frac{\alpha}{2}\right)\text{.}\) Then the interval:
+
+\begin{gather*} +\left[A_n - c_{\alpha} \left(\frac{s}{\sqrt{n}}\right), A_n + c_{\alpha} \left(\frac{s}{\sqrt{n}}\right)\right] +\end{gather*} +
+
is called a confidence interval with confidence level \(1 - \alpha\text{.}\) +
+
πŸ”—
+
+

+Example 4.3.3. +

+
Suppose measurements are taken of the heights of several plants in a garden plot. The measurements are given below. (Note: for the sake of a managable calculation, only five measurements are given. However, for TheoremΒ 4.2.1 to apply, the number of measurements would need to be greater.)
πŸ”—
+
Table 4.3.4. Plant Height Measurements
πŸ”—
+ + + + + + + + + + + + + + + + + + + + + + + + +
Plant \(i\) +Height \(H_i\) (in)
\(1\)\(9.2\)
\(2\)\(9.8\)
\(3\)\(10.1\)
\(4\)\(9.5\)
\(5\)\(10.4\)
+
Then the sample mean is:
+
+\begin{align*} +A_5 = \frac{H_1 + \dotsb + H_5}{5} \amp = \frac{9.2 + \dotsb + 10.4}{5} = 9.8. +\end{align*} +
+
The sum of the squares is:
+
+\begin{align*} +\sum H_i^2 \amp = H_1^2 + \dotsb + H_5^2 = 9.2^2 + \dotsb + 10.4^2 = 481.1 +\end{align*} +
+
So the sample variance is:
+
+\begin{gather*} +s^2 = \frac{\left(\sum H_i\right)^2 - 5 (A_5)^2}{5 - 1} = \frac{481.1 - 5(9.8)^2}{4} \approx 0.225 +\end{gather*} +
+
Now, the standard error of the mean is:
+
+\begin{gather*} +\frac{s}{\sqrt{n}} = \sqrt{\frac{0.225}{5}} \approx 0.212 +\end{gather*} +
+
Finally, we can give 95% confidence limits:
+
+\begin{align*} +\mu_{\ell} \amp = 9.8 - 1.96(0.212) \approx 9.38 \\ +\mu_{h} \amp = 9.8 + 1.96(0.212) \approx 10.22 +\end{align*} +
+
πŸ”—
+
+
πŸ”—
+
If the individual measurements \(X_1, \dotsc, X_n\) are indicator random variables, then the mean \(A_n\) represents the proportion which take on the value 1. For example, if the \(X_i\)’s indicate heads on coin flips, then \(A_n\) represents the proportion which come up heads. In this setting, we have a nice shortcut formula (ExampleΒ 3.2.7) for the variance of \(S_n = X_1 + \dotsc + X_n\text{.}\) We can make use of this formula to get the variance of \(A_n\) without going through the sample variance calculation above:
+
+\begin{align*} +\Var(S_n) \amp = np(1 - p) \\ +\Var(A_n) \amp = \Var\left(\frac{S_n}{n}\right) \\ +\amp = \frac{1}{n^2} \Var\left(S_n\right) \\ +\amp = \frac{1}{n^2} (np(1 - p)) \\ +\amp = \frac{p(1 - p)}{n}. +\end{align*} +
+
Since we won’t have access to the true value of \(p\text{,}\) we can use the maximum likelihood estimate \(\widehat{p}\text{.}\) +
+
πŸ”—
+
+

+Example 4.3.5. +

+
+
Suppose in a sample of 100 people, 40 have a particular trait. The maximum likelihood estimate for the probability \(p\) of a random person having the trait is \(\widehat{p} = \frac{40}{100} = 0.4\text{.}\) So the standard error will be:
+
+\begin{gather*} +\sqrt{\frac{(0.4)(1 - 0.4)}{100}} = \sqrt{\frac{0.24}{100}} \approx 0.049. +\end{gather*} +
+
Therefore, 95% confidence limits for \(p\) are:
+
+\begin{align*} +p_{\ell} \amp = 0.4 - 1.96(0.049) \approx 0.304 \\ +p_{h} \amp = 0.4 + 1.96(0.049) \approx 0.496 +\end{align*} +
+
πŸ”—
+
+
πŸ”—

Exercises Exercises

1.

Suppose we flip a coin 100 times and count 60 heads. Let \(p\) be the (unknown) probability that the coin comes up heads on a flip. Give an approximate 95% confidence interval for the value of \(p\text{.}\)
πŸ”—
+
Answer.
+
+\([0.504, 0.696]\text{.}\)
πŸ”—
+
+
πŸ”—
+
πŸ”—

3.

The weights of five mice are measured and recorded below. Give a 95% confidence interval for the sample mean weight of mice. (Pretend 5 measurements is large enough for the CLT to apply.)
πŸ”—
-
Table 4.3.1.
πŸ”—
+
Table 4.3.6.
πŸ”—
- - - - - - + - + + + + + + + + + + + + + -
mouse \(i\) +mouse \(i\) 12345weight \(W_i\) (g)
weight \(\widetilde{w}_i\) (g)1 26
2 32
3 33
4 20
5 29
πŸ”—

4.

+

Answer.
+
\([23.39, 32.61]\text{.}\)
πŸ”—
+
+
πŸ”—
+
+
πŸ”—

4.

The heights of five plants are measured and recorded below. Give a 95% confidence interval around the sample mean for the heights of the plants. (Pretend 5 measurements is large enough for the CLT to apply.)
πŸ”—
-
Table 4.3.2.
πŸ”—
+
Table 4.3.7.
πŸ”—
- - - - - - + - + + + + + + + + + + + + + -
plant \(i\) +plant \(i\) 12345height \(H_i\) (in)
height \(\widetilde{h}_i\) (in)1 15
2 14
3 18
4 21
5 17
πŸ”—
πŸ”—
πŸ”—
+
Answer.
+
\([14.61, 19.39]\text{.}\)
πŸ”—
+
+
πŸ”—
+
+
πŸ”—
πŸ”—
πŸ”—
PrevTopNext
diff --git a/sec-Continuous-RVs.html b/sec-Continuous-RVs.html index 1d6b9d9..60f41ad 100755 --- a/sec-Continuous-RVs.html +++ b/sec-Continuous-RVs.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-Correlation.html b/sec-Correlation.html index 0f55e49..b7d17ef 100755 --- a/sec-Correlation.html +++ b/sec-Correlation.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-Covariance.html b/sec-Covariance.html index dae1a36..e3d170f 100755 --- a/sec-Covariance.html +++ b/sec-Covariance.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-Discrete-RVs.html b/sec-Discrete-RVs.html index 384ce0e..e5d1339 100755 --- a/sec-Discrete-RVs.html +++ b/sec-Discrete-RVs.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-Expected-Value.html b/sec-Expected-Value.html index c9af030..7514dea 100755 --- a/sec-Expected-Value.html +++ b/sec-Expected-Value.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-Independent-Events.html b/sec-Independent-Events.html index fd8cd59..eb8eb7a 100755 --- a/sec-Independent-Events.html +++ b/sec-Independent-Events.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-Introduction.html b/sec-Introduction.html index d01deff..33223fb 100755 --- a/sec-Introduction.html +++ b/sec-Introduction.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-Joint-Distributions.html b/sec-Joint-Distributions.html index 75569c4..93f1707 100755 --- a/sec-Joint-Distributions.html +++ b/sec-Joint-Distributions.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-Likelihood.html b/sec-Likelihood.html index df0321b..bd5884c 100755 --- a/sec-Likelihood.html +++ b/sec-Likelihood.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-Linear-Regression.html b/sec-Linear-Regression.html index 9307ea4..eb68a0e 100755 --- a/sec-Linear-Regression.html +++ b/sec-Linear-Regression.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-One-Sample-Tests.html b/sec-One-Sample-Tests.html index 5d94b6c..1c9f047 100755 --- a/sec-One-Sample-Tests.html +++ b/sec-One-Sample-Tests.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-Power.html b/sec-Power.html index 6953e8d..1d60314 100755 --- a/sec-Power.html +++ b/sec-Power.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-Probability.html b/sec-Probability.html index 9016f53..f8930a1 100755 --- a/sec-Probability.html +++ b/sec-Probability.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-Set-Theory.html b/sec-Set-Theory.html index 33c075d..3fbb000 100755 --- a/sec-Set-Theory.html +++ b/sec-Set-Theory.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-Two-Sample-Tests.html b/sec-Two-Sample-Tests.html index b506685..5bc1f8e 100755 --- a/sec-Two-Sample-Tests.html +++ b/sec-Two-Sample-Tests.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - + diff --git a/sec-Variance.html b/sec-Variance.html index 09f851a..99a3f9f 100755 --- a/sec-Variance.html +++ b/sec-Variance.html @@ -101,14 +101,14 @@ eBookConfig.allow_pairs = false; eBookConfig.enableScratchAC = false; eBookConfig.build_info = ""; eBookConfig.python3 = null; -eBookConfig.runestone_version = '7.11.14'; +eBookConfig.runestone_version = '7.11.15'; eBookConfig.jobehost = ''; eBookConfig.proxyuri_runs = ''; eBookConfig.proxyuri_files = ''; eBookConfig.enable_chatcodes = false; - +