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@@ -1134,6 +1134,51 @@ var ptx_lunr_docs = [
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"title": "",
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"body": " Suppose a continuous random variable taking values in has cdf . Find the pdf . Find . "
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},
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{
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"id": "quiz-03",
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"level": "1",
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"url": "quiz-03.html",
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"type": "Worksheet",
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"number": "",
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"title": "Quiz 3",
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"body": " Quiz 3 The following work should be completed individually. Use of notes or textbooks is not allowed. You may use a scientific calculator, not a graphing calculator or phone app. Show all work unless instructed otherwise. Write either True or False for each of the following statements. No justification is required. Suppose a parameter has likelihood function with . Then the maximum likelihood estimation is . True. Suppose are random variables, and . Then, for sufficiently large , . False. Suppose we collect data to estimate the value of a parameter . Based on the collected data, we find a 95% confidence interval and a 90% confidence interval . Then . True. The heights of five plants are measured and recorded below. Find the sample mean, sample variance, and a 95% confidence interval around the sample mean for the heights of the plants. (Pretend that 5 measurements is enough for the CLT to apply.) Plant (in) Let be the average height of the sample. Then: So the 95% confidence limits are: Suppose a coin comes up heads with probability 0.6. We flip the coin 80 times, and let be the number of heads. Estimate . (Use a continuity correction if appropriate.) , so and . By the CLT, , so: Values 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 −1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 −1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 −1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 −1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 −1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 "
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},
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{
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"id": "quiz-03-3-1",
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"level": "2",
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"url": "quiz-03.html#quiz-03-3-1",
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"type": "Worksheet Exercise",
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"number": "1",
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"title": "",
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"body": " Write either True or False for each of the following statements. No justification is required. Suppose a parameter has likelihood function with . Then the maximum likelihood estimation is . True. Suppose are random variables, and . Then, for sufficiently large , . False. Suppose we collect data to estimate the value of a parameter . Based on the collected data, we find a 95% confidence interval and a 90% confidence interval . Then . True. "
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},
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{
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"id": "quiz-03-3-2",
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"level": "2",
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"url": "quiz-03.html#quiz-03-3-2",
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"type": "Worksheet Exercise",
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"number": "2",
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"title": "",
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"body": " The heights of five plants are measured and recorded below. Find the sample mean, sample variance, and a 95% confidence interval around the sample mean for the heights of the plants. (Pretend that 5 measurements is enough for the CLT to apply.) Plant (in) Let be the average height of the sample. Then: So the 95% confidence limits are: "
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},
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{
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"id": "quiz-03-4-1",
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"level": "2",
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"url": "quiz-03.html#quiz-03-4-1",
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"type": "Worksheet Exercise",
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"number": "3",
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"title": "",
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"body": " Suppose a coin comes up heads with probability 0.6. We flip the coin 80 times, and let be the number of heads. Estimate . (Use a continuity correction if appropriate.) , so and . By the CLT, , so: "
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},
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{
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"id": "quiz-03-4-2",
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"level": "2",
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"url": "quiz-03.html#quiz-03-4-2",
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"type": "Table",
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"number": "126",
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"title": "<span class=\"process-math\">\\(\\Phi(z)\\)<\/span> Values",
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"body": " Values 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 −1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 −1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 −1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 −1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 −1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 "
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},
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{
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"id": "exam-01",
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"level": "1",
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@@ -1265,7 +1310,7 @@ var ptx_lunr_docs = [
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"level": "2",
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"url": "recitation-calculus-review.html#thm-FTC",
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"type": "Theorem",
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"number": "126",
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"number": "127",
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"title": "Fundamental Theorem of Calculus.",
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"body": " Fundamental Theorem of Calculus If is an antiderivative of i.e., if then: "
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},
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