Question: Problem 3. Let X be a discrete random variable with probability mass function f(x) given bellow and f(x) = 0 for all other x. Let

Problem 3. Let X be a discrete random variable with probability

Problem 3. Let X be a discrete random variable with probability mass function f(x) given bellow and f(x) = 0 for all other x. Let the random variable Y be defined by Y-X, ie., if X 2, ten Y 4 x-1012 (a) What are the possible values of Y? (b) Calculate the probability mass function of Y? (c) Calculate the probabilities P(YsI), P(Ys3/4) and P(Y> 0). (d) Find the mean and variance of Y (e) Find the mean and variance of 3Y-2

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