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If X ~ Binomial (n, p) and Y ~ Binomial (m, p) are independent variables with...

If X ~ Binomial (n, p) and Y ~ Binomial (m, p) are independent variables with the same probability p, what is the distribution for Z=X+Y? Is it still a binomial distribution? Write out the pdf for Z if it is binomial, otherwise, explain why it is not. What about W = X-Y, is it a binomial distribution? Write out the pdf for W if it is binomial, otherwise, explain why it is not.

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