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You perform a sequence of m+n independent Bernoulli trials with success probability p between (0, 1)....

You perform a sequence of m+n independent Bernoulli trials with success probability
p between (0, 1). Let X denote the number of successes in the first m trials and Y be the number of
successes in the last n trials. Find f(x|z) = P(X = x|X + Y = z). Show that this function of x,
which will not depend on p, is a pmf in x with integer values in [max(0, z - n), min(z,m)].
Hint: the intersection of seemingly dependent events {X = x} and {X + Y = z} can be written as the intersection of independent events {X = x} and {Y = z - x}.

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