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1. An electronic system has two different types of components in joint operation. Let X1 and...

1. An electronic system has two different types of components in joint operation. Let X1 and X2 denote the Random Length of life in hundreds of hours of the components of Type I and Type II (Type 1 and Type 2), respectively. Suppose that the joint probability density function (pdf) is given by

f(x1, x2) = { (1/8)y1 e^-(x1 + x2)/2, x1 > 0, x2 > 0

0 Otherwise.

a.) Show that X1 and X2 are independent.

b.) Find E(Y1+Y2) and variance Var(Y1+Y2).

c.) Find E(X2 | X1).

d.) Express P(X1 + X2 < 1) as a double integral; there is no need to evaluate it.

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