Math

StatisticsProbability and Statistics for Engineering and the SciencesTwo 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?BuyFind*launch*

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*:

**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 Engineering and the Sciences

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Suppose the distribution is...Ch. 5.4 - The National Health Statistics Reports dated Oct....Ch. 5.4 - There are 40 students in an elementary statistics...Ch. 5.4 - Let X denote the courtship time for a randomly...Ch. 5.4 - The time taken by a randomly selected applicant...Ch. 5.4 - The lifetime of a certain type of battery is...Ch. 5.4 - Rockwell hardness of pins of a certain type is...Ch. 5.4 - Suppose the sediment density (g/cm) of a randomly...Ch. 5.4 - The number of parking tickets issued in a certain...Ch. 5.4 - A binary communication channel transmits a...Ch. 5.4 - Suppose the distribution of the time X (in hours)...Ch. 5.5 - A shipping company handles containers in three...Ch. 5.5 - Let X1, X2, and X3 represent the times necessary...Ch. 5.5 - Refer back to Example 5.31. Two cars with...Ch. 5.5 - Exercise 26 introduced random variables X and Y,...Ch. 5.5 - Manufacture of a certain component requires three...Ch. 5.5 - Refer to Exercise 3. a. 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A...Ch. 5 - If the amount of soft drink that I consume on any...Ch. 5 - Refer to Exercise 58, and suppose that the Xis are...Ch. 5 - A student has a class that is supposed to end at...Ch. 5 - Garbage trucks entering a particular...Ch. 5 - Each customer making a particular Internet...Ch. 5 - a. Use the general formula for the variance of a...Ch. 5 - Suppose a randomly chosen individuals verbal score...Ch. 5 - a. Let X1 have a chi-squared distribution with...Ch. 5 - a. Show that Cov(X, Y + Z) = Cov(X, Y) + Cov(X,...Ch. 5 - A rock specimen from a particular area is randomly...Ch. 5 - Let A denote the percentage of one constituent in...Ch. 5 - Let X1, . . . , Xn be independent rvs with mean...Ch. 5 - A more accurate approximation to E[h(X1, . . . ,...Ch. 5 - Let X and Y be independent standard normal random...Ch. 5 - Let X1, X2, . . . , Xn be random variables...

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