Hw04 - STAT 410 Homework #4 (due Friday, February 15, by...

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STAT 410 Spring 2008 Homework #4 (due Friday, February 15, by 4:00 p.m.) 1. Let X and Y be independent random variables, each geometrically distributed with the probability of “success” p , 0 < p < 1. That is, p X ( k ) = p Y ( k ) = ( ) 1 1 - - k p p , k = 1, 2, 3, … , a) Find P ( X > Y ). [ Hint: First, find P ( X = Y ). ] b) Find P ( X + Y = n ), n = 2, 3, 4, … , and P ( X = k | X + Y = n ), k = 1, 2, 3, … , n – 1. From the textbook: 2.3.3 Let f ( x 1 , x 2 ) = 3 2 2 1 21 x x , 0 < x 1 < x 2 < 1, zero elsewhere, be the joint pdf of X 1 and X 2 . (a) Find the conditional mean and variance of X 1 , given X 2 = x 2 , 0 < x 2 < 1. (b) Find the distribution of Y = E ( X 1 | X 2 ). (c) Determine E ( Y ) and Var ( Y ) and compare these to E ( X 1 ) and Var ( X 1 ), respectively. 2.3.10 Let X 1 and X 2 have joint pmf p ( x 1 , x 2 ) described as follows: ( x 1 , x 2 ) ( 0, 0 ) ( 0, 1 ) ( 1, 0 ) ( 1, 1 ) ( 2, 0 ) ( 2, 1 ) p ( x 1 , x 2
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Hw04 - STAT 410 Homework #4 (due Friday, February 15, by...

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