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Unformatted text preview: E ( X ) = ∞ s k =0 P ( X > k ) 5. The random variable X takes the values 0 , 1 ,... with P ( X = k ) = p k . Let Y = ( X1) u ( X1) where u ( . ) denotes the unit step function. Express E ( Y ) and E ( Y 2 ) in terms of E ( X ) and E ( X 2 ). 6. A newly married couple decides to continue having children until they have one of each sex. If the events of having a boy and a girl are independent and equiprobable, how many children should this couple expect? 2 7. A drunken man has n keys, one of which opens the door to his oFce. He tries the keys at random, one by one, and independently. Compute the mean and the variance of the number of trials required to open the door if the wrong keys (a) are not eliminated; (b) are eliminated. 3...
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 Spring '09
 Champagne
 random variable X., Trottier

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