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

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 < 2X2) and P (X1 = 2X2). (b) Determine the mgf of X1+2X2+X3. Are X1, X2, and X3 random variables independent? Give reasoning.

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