Question: Suppose X and Y are random variables with P (X = 1) = P (X = -1) = 1 2; P (Y = 1) =

Suppose X and Y are random variables with

P (X = 1) = P (X = -1) = 1 2; P (Y = 1) = P (Y = -1) = 1 2. Let c = P (X = 1 and Y = 1).

(a) Determine the joint distribution of X and Y , Cov(X, Y ), and Cor(X, Y ).

(b) For what value(s) of c are X and Y independent? For what value(s) of c are X and Y 100% correlated?

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