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 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 
.
d. Find 
.
e. Find P(X+Y ? 2).
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