A chicken lays a Pois() number N of eggs. Each egg hatches a chick with probability p

Chapter 7, Problem 48

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A chicken lays a Pois() number N of eggs. Each egg hatches a chick with probability p, independently. Let X be the number which hatch, so X|N = n Bin(n, p). Find the correlation between N (the number of eggs) and X (the number of eggs which hatch). Simplify; your final answer should work out to a simple function of p (the should cancel out).

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