Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Question
Chapter 6.5, Problem 39E
To determine
Obtain the density
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6.25 In Exercise 6.11, we considered two electronic components that operate independently, each
with life length governed by the exponential distribution with mean 1. We proceeded to use
the method of distribution functions to obtain the distribution of the average length of life for
the two components. Use the method of transformations to obtain the density function for the
average life length of the two components.
Consider two components whose lifetimes X, and
X2 are independent and exponentially distributed
with parameters and 22, respectively. Obtain
the joint pdf of total lifetime X, + X2 and the
proportion of total lifetime X,/(X, + X2) during
which the first component operates.
a and d only pls
Chapter 6 Solutions
Mathematical Statistics with Applications
Ch. 6.3 - Let Y be a random variable with probability...Ch. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - The amount of flour used per day by a bakery is a...Ch. 6.3 - Prob. 5ECh. 6.3 - The joint distribution of amount of pollutant...Ch. 6.3 - Suppose that Z has a standard normal distribution....Ch. 6.3 - Assume that Y has a beta distribution with...Ch. 6.3 - Prob. 9ECh. 6.3 - The total time from arrival to completion of...
Ch. 6.3 - Suppose that two electronic components in the...Ch. 6.3 - Prob. 12ECh. 6.3 - If Y1 and Y2 are independent exponential random...Ch. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Prob. 17ECh. 6.3 - A member of the Pareto family of distributions...Ch. 6.3 - Prob. 19ECh. 6.3 - Let the random variable Y possess a uniform...Ch. 6.3 - Prob. 21ECh. 6.4 - Prob. 23ECh. 6.4 - In Exercise 6.4, we considered a random variable Y...Ch. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6.4 - Let Y have a uniform (0, 1) distribution. Show...Ch. 6.4 - Prob. 29ECh. 6.4 - A fluctuating electric current I may be considered...Ch. 6.4 - The joint distribution for the length of life of...Ch. 6.4 - Prob. 32ECh. 6.4 - The proportion of impurities in certain ore...Ch. 6.4 - A density function sometimes used by engineers to...Ch. 6.4 - Prob. 35ECh. 6.4 - Refer to Exercise 6.34. Let Y1 and Y2 be...Ch. 6.5 - Let Y1, Y2,, Yn be independent and identically...Ch. 6.5 - Let Y1 and Y2 be independent random variables with...Ch. 6.5 - Prob. 39ECh. 6.5 - Prob. 40ECh. 6.5 - Prob. 41ECh. 6.5 - A type of elevator has a maximum weight capacity...Ch. 6.5 - Prob. 43ECh. 6.5 - Prob. 44ECh. 6.5 - The manager of a construction job needs to figure...Ch. 6.5 - Suppose that Y has a gamma distribution with =...Ch. 6.5 - A random variable Y has a gamma distribution with ...Ch. 6.5 - Prob. 48ECh. 6.5 - Let Y1 be a binomial random variable with n1...Ch. 6.5 - Let Y be a binomial random variable with n trials...Ch. 6.5 - Prob. 51ECh. 6.5 - Prob. 52ECh. 6.5 - Let Y1,Y2,,Yn be independent binomial random...Ch. 6.5 - Prob. 54ECh. 6.5 - Customers arrive at a department store checkout...Ch. 6.5 - The length of time necessary to tune up a car is...Ch. 6.5 - Prob. 57ECh. 6.5 - Prob. 58ECh. 6.5 - Prob. 59ECh. 6.5 - Prob. 60ECh. 6.5 - Prob. 61ECh. 6.5 - Prob. 62ECh. 6.6 - In Example 6.14, Y1 and Y2 were independent...Ch. 6.6 - Refer to Exercise 6.63 and Example 6.14. Suppose...Ch. 6.6 - Prob. 65ECh. 6.6 - Prob. 66ECh. 6.6 - Prob. 67ECh. 6.6 - Prob. 68ECh. 6.6 - Prob. 71ECh. 6 - Let Y1 and Y2 be independent and uniformly...Ch. 6 - As in Exercise 6.72, let Y1 and Y2 be independent...Ch. 6 - Let Y1, Y2,, Yn be independent, uniformly...Ch. 6 - Prob. 75SECh. 6 - Prob. 76SECh. 6 - Prob. 77SECh. 6 - Prob. 78SECh. 6 - Refer to Exercise 6.77. If Y1,Y2,,Yn are...Ch. 6 - Prob. 80SECh. 6 - Let Y1, Y2,, Yn be independent, exponentially...Ch. 6 - Prob. 82SECh. 6 - Prob. 83SECh. 6 - Prob. 84SECh. 6 - Let Y1 and Y2 be independent and uniformly...Ch. 6 - Prob. 86SECh. 6 - Prob. 87SECh. 6 - Prob. 88SECh. 6 - Let Y1, Y2, . . . , Yn denote a random sample from...Ch. 6 - Prob. 90SECh. 6 - Prob. 91SECh. 6 - Prob. 92SECh. 6 - Prob. 93SECh. 6 - Prob. 94SECh. 6 - Prob. 96SECh. 6 - Prob. 97SECh. 6 - Prob. 98SECh. 6 - Prob. 99SECh. 6 - The time until failure of an electronic device has...Ch. 6 - Prob. 101SECh. 6 - Prob. 103SECh. 6 - Prob. 104SECh. 6 - Prob. 105SECh. 6 - Prob. 106SECh. 6 - Prob. 107SECh. 6 - Prob. 108SECh. 6 - Prob. 109SECh. 6 - Prob. 110SECh. 6 - Prob. 111SECh. 6 - Prob. 112SECh. 6 - Prob. 113SECh. 6 - Prob. 114SECh. 6 - Prob. 115SECh. 6 - Prob. 116SE
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