Question: There are two fuses in an electrical device. Let X denotes the lifetime of the first fuse, and let Y denote the lifetime of the

There are two fuses in an electrical device. Let X denotes 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

a. Find P(X < 2 and Y < 3).
b. Find the probability that both fuses last at least 3 years.
c. Find the marginal probability density function of X.
d. Find the marginal probability density function of Y.
e. Are X and Y independent? Explain.

e-2-3/3 0 and y>0 e-1/2-y/J f(x,y) f(x,y) = 6 otherwise

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