A discrete random variable y takes the value -1 0 and 1, Ask an Expert

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A discrete random variable Y takes the value -1, 0 and 1 with probabilities 1/2θ, 1- θ and 1/2θ respectively. Let Y1 and Y2 be two independent random variables, each with the same distribution as Y.

a) By listing the set of possible values of (Y1, Y2) find the joint probability distribution function Pr(Y1 = y1, Y2 = y2). Verify that this is a valid probability mass function.

b) Find the sampling distribution of (Y2 - Y1)^2

c) SHow that X = 1/2(Y2 - Y1)^2 is an unbiased estimator for θ, i.e. E(X) = θ

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