Question

A6. Let X and Y be two independent, nonnegative integer-valued random variables whose

distribution has the property

P (X = x|X + Y = x + y) =

m

x

n

y

m+n

x+y

for all nonnegative integers x and y where m and n are given positive integers. Assume

that P(X = 0) and P(Y = 0) are strictly positive. Show that both X and Y have

binomial distributions with the same parameter p, the other parameters being m and

n respectively.

Answer 1

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