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hw3 - STAT 225 Homework 3 Due Friday May 29 Comments 1 This...

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STAT 225 - Homework 3 Due Friday May 29 Comments: 1. This homework is due Friday, May 29 in class, BEFORE class starts. 2. Please remember staple if you turn in more than one page. 3. You must always SHOW ALL WORK. If you do not show your work, you may not receive full credit. Do the following problems. 1. Page 97, problem 3.12 2. We say that the random variable Y is uniform on the numbers 1 , 2 , . . . , k if: P Y ( y ) = 1 k y = 1 , 2 , . . . k Find E ( Y ) and V ( Y ). Useful facts: n X i =1 i = n ( n + 1) 2 n X i =1 i 2 = n ( n + 1)(2 n + 1) 6 3. Page 100, problem 3.33 Note: We showed part (a) in lecture 7, so you only need to do part (b). Guidance: For part (b), you can proceed in one of the following two ways: V ( aY + b ) = (by definition of variance) = E [( aY + b ) - E ( aY + b )] 2 . Now apply part (a), and go from there .... V ( aY + b ) = (by theorem 4 in lecture 7) = E ( aY + b ) 2 - E 2 ( aY + b ). Now apply part (a), and go from there .... 4. The number of sales that a telemarketing salesperson does in an hour is a random variable X having a mean value of μ X = 3 . 5, and variance σ 2 X = 1 . 25.
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