Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y : f ( x , y ) = { x e − x ( 1 + y ) x ≥ 0 and y ≥ 0 0 otherwise a. What is the probability that the lifetime X of the first component exceeds 3? b. What are the marginal pdf’s of X and Y ? Are the two lifetimes independent? Explain. c. What is the probability that the lifetime of at least one component exceeds 3?


Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809

Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809


Chapter 5.1, Problem 12E
Textbook Problem

Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y:

     f ( x , y ) = { x e x ( 1 + y ) x 0 and  y 0 0 otherwise

  1. a. What is the probability that the lifetime X of the first component exceeds 3?
  2. b. What are the marginal pdf’s of X and Y? Are the two lifetimes independent? Explain.
  3. c. What is the probability that the lifetime of at least one component exceeds 3?

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Chapter 5 Solutions

Probability and Statistics for Engineering and the Sciences
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