Question: The lifetime of a certain component, in years, has probability density function. Two such components, whose lifetimes are independent, are available. As soon as the

The lifetime of a certain component, in years, has probability density function.

-Ә |f(x) ) = х <0

Two such components, whose lifetimes are independent, are available. As soon as the first component fails, it is replaced with the second component. Let X denote the lifetime of the first component, and let Y denote the lifetime of the second component.

a. Find the joint probability density function of X and Y.

b. Find P(X ‰¤ 1 and Y > 1).

c. Find Î¼_X.

d. Find Î¼_X+Y.

e. Find P(X + Y ‰¤ 2). Sketch the region of the plane where x + y ‰¤ 2, and then integrate the joint probability density function over that region.

- |f(x) ) =

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