Let X and Y be independent exponential random variables with respective rates and , where >.

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

(b) Use part

(a) to find E[X|X +Y = c].

(c) Find E[Y|X +Y = c].

Transcribed Image Text:

fx|x+x(x|c) = (-l)e-(-)x 1-e-(-)c 0