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Let A and B be independent Poisson random variables with parameters α and β, respectively. Find the conditional expectation of A given A + B = c.

(Hint: For discrete random variables, there is no conditional density. Use the definition of conditional probability.)

Attempt:

Starting with the definition, f(A | A + B = c) = [f(A, A+B=c)] / [f(A+B=c)]

Not sure how to proceed.