Concept explainers
The lifetime of a certain component, in years, has
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 μX.
- d. Find μX+Y.
- e. Find P(X + Y ≤ 2). (Hint: Sketch the region of the plane where x + y ≤ 2, and then integrate the joint probability density function over that region.)
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