There are two fuses in an electrical device. Let X denote the lifetime of the first fuse, and let Y denote the lifetime of the second fuse (both in years). Assume the joint probability density function of X and Y is e-x/2-y/3 6. x > 0 and y > 0 f(x,y) = otherwise Find P(X < 2and Y < 3). a. b. Find the probability that both fuses last at least 3 years. Find the marginal probability density function of X. Find the marginal probability density function of Y. Are X and Y independent? Explain. C. d. e.

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