Let X. Y, and Z be independent random variables, where X

Chapter , Problem 36

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Let X. Y, and Z be independent random variables, where X is Bernoulli with parameter 1/3, Y is exponential with parameter 2, and Z is Poisson with parameter 3. (a) Consider the new random variable U = XY + (1 - X)Z. Find the transform associated with U. (b) Find the transform associated with 2Z + 3. (c) Find the transform associated with Y + Z.

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