Question

Let X 1 and X 2 have the joint probability distribution function ??(??1, ??2) = � ??−(??1+??2) ??1 > 0, ??2 > 0 0 elsewhere Find ??(??1 + ??2) and ??(??1 + ??2).

Answer 1

The marginal pdf of X2 is

The marginal pdf of X1 is

Since

So X1 and X2 are independent.

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The marginal pdfs of X1 and X2 are exponential distribution with parameter 1. So,

Since X1 and X2 are independent so