Let X be the lifetime of an electronic system and Y be the lifetime of one of its components. Suppose that the electronic system fails if the component does (but not necessarily vice versa). Furthermore, suppose that the joint probability density function of X and Y (in years) is given by

(a) Determine the expected value of the remaining lifetime of the component when the system dies.

(b) Find the covariance of X and Y .

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f(x, y) = 49 e -y/7 if 0xy