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# lecture17_6slides - Statistics 528 Lecture 17 Rules for...

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Statistics 528 - Lecture 17 1 Statistics 528 - Lecture 17 Prof. Kate Calder 1 Rules for Means of Random Variables Rule 1 If X is a random variable and a and b are fixed numbers, then a+bx = a+b X Rule 2 If X and Y are random variables, then X+Y = X + y Statistics 528 - Lecture 17 Prof. Kate Calder 2 Variance of a Discrete Random Variable Suppose that X is a discrete random variable whose distribution is Value of X x 1 x 2 x 3 x k Probability p 1 p 2 p 3 p k and that X is the mean of X. The variance of X is ± 2 X = (x 1 - X ) 2 p 1 + (x 2 - X ) 2 p 2 + +(x- X ) 2 p k ² (x i - X ) 2 p i The standard deviation of X is the square root of the variance. Statistics 528 - Lecture 17 Prof. Kate Calder 3 Example: Free-Throw (Lecture 16) What is the standard deviation of shots made by a 58% shooter who shoots three shots? The probability distribution for X (number of shots made): x P(X=x) 0 0.08 1 0.1+0.1+0.1=0.3 2 0.14+0.14+0.14 = 0.42 3 0.2 Statistics 528 - Lecture 17

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lecture17_6slides - Statistics 528 Lecture 17 Rules for...

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