Question: Problem 5 [15pts] Let X be a random variable with uniform distribution over the interval [0,2], and let Y be a random variable that

Problem 5 [15pts] Let X be a random variable with uniform distribution over the interval [0,2], and let Y be a random variable that is independent with X such that 1, with probability > Y = 3, with probability // Let Z = XY. (a) Find the unconstrained MMSE estimate of Z based on the observation of X. (b) Find the linear MMSE estimate of Z based on the observation of X. (c) Find the linear MMSE estimate of Z based on the observation of X and Y. (d) Find the unconstrained MMSE estimate of X based on the observation of Z.

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