160a09_hw1

160a09_hw1 - Y given X = i 4 Find P Y = 0 and P Y = 1...

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Pstat160A Winter 2009 Hw #1 Due: Friday, Jan 16 This is the theoretical part of the homework for week #1, to be submitted at the beginning of class on Friday. In addition, you need to send by email the Matlab homework that can be fond on the class webpage. Problem 1: Let X and Y be two discrete random variables with values 0 , 1 , ··· , having joint distribution p X,Y ( i,j ) = P ( X = i, Y = j ) = e - λ λ i ( i + 1)! for i 0 , 0 j i. 1) Are X and Y independent? Why? 2) Find the marginal distribution of X . 3) Find the conditional distribution of
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Unformatted text preview: Y given X = i . 4) Find P ( Y = 0) and P ( Y = 1) Problem 2: Problem 29, p. 89. Hint: After a flip, what is the probability that the next flip is a change over? (very simple solution!) Problem 3: Problem 56, p. 93. Hint: Use the trick X = ∑ i X i we used for Binomial and Hypergeometric. Here let X i = 1 if there is at least one coupon of type i . You will need to find the probability that this event occurs. Problem 4: Problem 71, p. 95....
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