Chapter 24, PROBLEM SET 24.9 #14

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An electronic device consists of two components. Let X and Y [years] be the times to failure of the first and second components, respectively. Assume that (X, Y) has the density f(x, y) = 4e^{-2(x+y)} if x > 0 and y > 0 and 0 otherwise.

(a) Are X and Y dependent or independent? (b) Find the densities of the marginal distributions.

(c) What is the probability that the first component will have a lifetime of 2 years or longer?

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