Question: Let X1 and X2 be independent random variables each having the probability distribution f(x) = ex, x> 0, 0, elsewhere. Show that the random variables

Let X1 and X2 be independent random variables each having the probability distribution f(x) = e−x, x> 0, 0, elsewhere.

Show that the random variables Y1 and Y2 are independent when Y1 = X1 + X2 and Y2 = X1/(X1 + X2).

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