Question: Let f(x 1 , x 2 , x 3 ) = exp[(x 1 + x 2 + x 3 )], 0 < x 1 <

Let f(x1, x2, x3) = exp[−(x1 + x2 + x3)], 0 < x1 < ∞, 0 < x2 < ∞, 0 < x3 < ∞, zero elsewhere, be the joint pdf of X1, X2, X3.

(a) Compute P(X1 < X2 < X3) and P(X1 = X2 < X3).

(b) Determine the joint mgf of X1,X2, and X3. Are these random variables independent?

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