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Unformatted text preview: E120 Homework 4 Due 07/29/2010 Problem 1: Let Z be a random variable with probability mass function p ( ) such that p (0) = 0 . 1, p (1) = 0 . 3, p (2) = 0 . 3, p (3) = 0 . 1, and p (4) = 0 . 2. 1. Find E [ Z ] 2. Find E [ Z E [ Z ]] 3. Find E [ Z 2 ] 4. Find E [ Z 3 ] 5. Find E [sin( Z ) + 2 Z ] 6. Find E [( Z E [ Z ]) 2 ] 7. Find Var[ Z ] Problem 2: Suppose that X and Y are random variables such that var [ X ] = var [ Y ] = cov [ X,Y ] = 1, find 1. var (3 X ) 2. var (2 X + 4) 3. var ( X Y ) 4. cov ( X,X ) 5. cov ( X,X + Y ) 6. var (4 X + Y 7) Problem 3: Two balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls. Suppose that we win $2 for each black ball selected and we lose $1 for each white ball selected, and nothing happens when we picked an orange ball. Let X denote our winnings. What are the possible values of X, and what are the probabilities associated with each value? Problem 4: Suppose that you are flipping 5 biased coins independently from one another. The prob ability of a coin landing HEAD is 0...
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 Summer '11
 ALDER

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