diff --git a/source/main.ptx b/source/main.ptx index 05b796d..0ea7f5f 100644 --- a/source/main.ptx +++ b/source/main.ptx @@ -28,6 +28,7 @@ + @@ -44,5 +45,14 @@ + + + Exam Review + + + + + + \ No newline at end of file diff --git a/source/notes/2-3.ptx b/source/notes/2-3.ptx new file mode 100644 index 0000000..288fe9c --- /dev/null +++ b/source/notes/2-3.ptx @@ -0,0 +1,41 @@ + + +
+ Tuesday, Feb 3 + + +

+ This is an outline of the topics we covered in class. + These notes are not a substitute for your own note-taking. + I highly recommend that you take your own notes during class. + If you ever miss a class for any reason, reach out to another student in class to get a copy of their notes. +

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+ + + + Variance + +

+ Question: How spread out are X values? One answer we might try is to measure the average distance from the average value: + + \E\left[|X - \E(X)|\right] + + To simplify notation, we'll write \mu = \E(X). + Also, it's often usefull to square a term rather than take absolute value when we want to ensure a positive output, so we'll define... +

+ + + +

+ Let X be a random variable with \E(X) = \mu. + The variance of X is: + + \sigma^2 = \Var(x) = \E\left[ (X - \mu)^2\right] + + \sigma = \sqrt{\Var(X)} is called the standard deviation. +

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\ No newline at end of file diff --git a/source/quizzes/quiz-02.ptx b/source/quizzes/quiz-02.ptx index 16a4d1f..c4fbf32 100644 --- a/source/quizzes/quiz-02.ptx +++ b/source/quizzes/quiz-02.ptx @@ -140,7 +140,16 @@

- \Pr(X = 2, Y = 0) = 0.2 , and \Pr(X = 2)\Pr(Y = 0) = (0.4)(0.25) = 0.1. Since 0.2 \neq 0.1, X and Y are not independent. + Checking each cell in the table: + + \Pr(X = 0, Y = 0) \amp = 0.1 = (0.4)(0.25) = \Pr(X = 0)\Pr(Y = 0) + \Pr(X = 1, Y = 0) \amp = 0.05 = (0.2)(0.25) = \Pr(X = 1)\Pr(Y = 0) + \Pr(X = 2, Y = 0) \amp = 0.1 = (0.4)(0.25) = \Pr(X = 2)\Pr(Y = 0) + \Pr(X = 0, Y = 1) \amp = 0.3 = (0.4)(0.75) = \Pr(X = 0)\Pr(Y = 1) + \Pr(X = 1, Y = 1) \amp = 0.15 = (0.2)(0.75) = \Pr(X = 1)\Pr(Y = 1) + \Pr(X = 2, Y = 1) \amp = 0.3 = (0.4)(0.75) = \Pr(X = 2)\Pr(Y = 1) + + So X, Y are independent.

diff --git a/source/review/Exam-1-Review.ptx b/source/review/Exam-1-Review.ptx new file mode 100644 index 0000000..aed9e5f --- /dev/null +++ b/source/review/Exam-1-Review.ptx @@ -0,0 +1,36 @@ + + +
+ Exam 1 Review + + +

+ Use the following problems to prepare for the exam. + There will be in-class review on Thursday, February 12. + Your recitation this week will also be exam review. +

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+ + + + Allowed Materials + +

+ You will be allowed to use a scientific calculator (not a graphing calculator, not a calculator app on your phone). + You may not share a calculator with another student; you must use your own calculator. +

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+ You may bring a standard 3 in x 5 in index card with prepared notes. + You may use both sides of the notecard. + You must put your full name in the top right corner of the card, and turn it in along with your exam. +

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