Question: Random variables X, X, have a bivariate Poisson distribution if PIX, X, for any pair of nonnegative integers (k), where a,, . are nonnegative param-

Random variables X, X, have a bivariate Poisson distribution if PIX, X, for any pair of nonnegative integers (k), where a,, . are nonnegative param- eters. Define a probability space and rvs X. X, on it whose joint distribution is bivariate Poisson and show that X, is a Poisson rv with mean a,+Prove that the correlation (XX) 20 and that X, and X, are independent iffa

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