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

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 denotes 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 Î¼X.
d. Find Î¼X+Y.
e. Find P(X + Y ‰¤ 2).

610 5 f (x) = 0 X 0

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