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Unformatted text preview: V AR [ T ]. 4. (2 pts) (Textbook exercise 4.39) Let X , Y , and Z have joint pdf f X,Y,Z ( x, y, z ) = k ( x + y + z ) x 1 , y 1 , z 1 , a. Find k . b. Find f Z ( z  x, y ). 5. (2 pts) (Textbook exercise 4.45) The number N of customer arrivals at a service station is a Poisson random variable with mean customers per second. There are four types of customers. Let X k be the number of type k arrivals. Suppose P [ X 1 = k 1 , X 2 = k 2 , X 3 = k 3  N = n ] = p ( k 1 , k 2 , k 3 ) = n ! p k 1 1 p k 2 2 p k 3 3 (1p 1p 2p 3 ) nk 1k 2k 3 k 1 ! k 2 ! k 3 !( nk 1k 2k 3 )! a. Find the joint pmf of ( N, X 1 , X 2 , X 3 ). b. Find the marginal pmf of ( X 1 , X 2 , X 3 ). 1...
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 Fall '08
 GELFAND

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