Question: Let X and Y be independent exponential random variables with respective rates and , where >. Let c > 0. (a) Show that the

Let X and Y be independent exponential random variables with respective rates

λ and μ, where λ>μ. Let c > 0.

(a) Show that the conditional density function of X, given that X + Y =

c, is fX|X+Y (x|c) = (λ − μ)e−(λ−μ)x 1 − e−(λ−μ)c , 0 < x < c

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