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1. Suppose A and B are independent events with probabilities P(A) = 1/2 and P(B) =...

1. Suppose A and B are independent events with probabilities P(A) = 1/2 and P(B) = 1/3. Define random variables X and Y by X =Ia+Ib, Y=Ia-Ib, where Ia, Ib are indicator functions (a) What is the joint distribution of X and Y? (b) What is P(X less than 2, Y greater than or equal to zero), (c) Are X and Y independent, Justify

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