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# worksheet10 - Stat 400 In Class Worksheet 10 T.A Emily King...

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Stat 400 In Class Worksheet 10 T.A. Emily King April 16, 2008 1. (Modified from book p. 202 # 27) Annie and Alvie have agreed to meet for lunch between noon (0:00 PM) and 1:00 PM. Denote Annie’s arrival time by X , Alvie’s by Y and suppose that X and Y are independent with pdf’s f X ( x ) = 3 x 2 0 x 1 0 o.w. f Y ( y ) = 2 y 0 y 1 0 o.w. Set up, but do not solve, the integral to compute the expected amount of time that the one who arrives first must wait for the other person. Also, what is ρ ? 2. (Book Example 5.18) Let X and Y be discrete rv’s with joint pmf p ( x, y ) = 1 4 ( x, y ) = ( - 4 , 1) , (4 , 1) , (2 , 2) , ( - 2 , - 2) 0 o.w. What is the covariance of X and Y ? 3. (Modified from book p. 212 # 41) Let X be the number of packages being mailed to a randomly selected customer at a certain shipping facility. Supposed the distribution of X is as follows: x 1 2 3 p ( x ) . 5 . 3 . 2 (a) Consider a random sample of size n = 2 and let

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