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Let N be a random variable that takes values in the non-negative integers 0, 1, 2, . . . . Given that N = n,

Let N be a random variable that takes values in the non-negative integers 0, 1, 2, . . . .

Given that N = n, toss a fair coin n times, and let X be the number of Heads and Y = N X the number of Tails.

What is the covariance of X and Y if

(a) N has the Poisson distribution with parameter > 0?

(b) N has the geometric distribution P{N = k} = r k1 (1 r)?

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