Suppose that Y is a binomial random variable based on n trials with success probability

Chapter 3, Problem 3.54

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Suppose that Y is a binomial random variable based on n trials with success probability p and consider Y = n Y . a Argue that for y = 0, 1,..., n P(Y = y ) = P(n Y = y ) = P(Y = n y ). b Use the result from part (a) to show that P(Y = y ) = n n y pny qy = n y qy pny . c The result in part (b) implies that Y has a binomial distribution based on n trials and success probability p = q = 1 p. Why is this result obvious? 3.

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