Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)
10th Edition
ISBN: 9780137538461
Author: Robert Hogg, Elliot Tanis
Publisher: PEARSON+
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 5.3, Problem 16E
The lifetime in months of a certain part has a gamma distribution with
A company buys three such parts and uses one until it fails, replacing it with a second part. When the latter fails, it is replaced by the third part. What are the mean and the variance of the total lifetime (the sum of the lifetimes of the three parts) associated with this situation?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Chapter 5 Solutions
Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)
Ch. 5.1 - Let X have a geometric distribution with parameter...Ch. 5.1 - Suppose that X is a continuous random variable...Ch. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Let X have a gamma distribution with =3 and =2....Ch. 5.1 - The pdf of X is f(x)=2x,0x1. (a) Find the cdf of...Ch. 5.1 - Prob. 7ECh. 5.1 - Let X have a logistic distribution with pdf...Ch. 5.1 - A sum of $50000 is invested at a rate R, selected...Ch. 5.1 - The lifetime (in years) of a manufactured product...
Ch. 5.1 - Statisticians frequently use the extreme extreme...Ch. 5.1 - Prob. 12ECh. 5.1 - Let X have a Cauchy distribution. Find (a) P(X1)....Ch. 5.1 - Let f(x)=1[(1+x2)],x, be the pdf of the Cauchy...Ch. 5.1 - If X is N(,2), then M(t)=E(etX)=exp(t+2t22),t. We...Ch. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - (a) Let X be a continuous random variable with...Ch. 5.2 - Let X1,X2, denote two independent random...Ch. 5.2 - Let X1 and X2 be independent chi-square random...Ch. 5.2 - Prob. 3ECh. 5.2 - Let the distribution of W be F(9, 24). Find the...Ch. 5.2 - Let the distribution of W be F(8. 4). Find the...Ch. 5.2 - Let X1 and X2 have independent gamma distributions...Ch. 5.2 - Let X1 and X2 be independent chi-square random...Ch. 5.2 - Let X have a beta distribution with parameters ...Ch. 5.2 - Determine the constant c such that...Ch. 5.2 - When and are integers and0p1, we have...Ch. 5.2 - Evaluate 00.4(7)(4)(3)y3(1y)2dy (a) Using...Ch. 5.2 - Let W1,W2 be independent, each with a Cauchy...Ch. 5.2 - Let X1, X2 be independent random variables...Ch. 5.2 - Prob. 14ECh. 5.2 - In Example 5.2-6, verify that the given...Ch. 5.2 - Show that if W has an F(r1,r2) distribution, then...Ch. 5.2 - Let W have an F distribution with parameters r1...Ch. 5.3 - Let X1 and X2 be independent Poisson random...Ch. 5.3 - Let X1 and X2 be independent random variables with...Ch. 5.3 - Let X1 and X2 be independent random variables with...Ch. 5.3 - Let X1 and X2 be a random sample of size n=2 from...Ch. 5.3 - Let X1 and X2 be observations of a random sample...Ch. 5.3 - Let X1 and X2 be a random sample of size n=2 from...Ch. 5.3 - The distributions of incomes in two Cities follow...Ch. 5.3 - Prob. 8ECh. 5.3 - Let X1,X2,...Xn be a random sample (of size n)...Ch. 5.3 - Let X1,X2,X3 denote a random sample of size n= 3...Ch. 5.3 - Let X1,X2,X3 be three independent random variables...Ch. 5.3 - Let X1,X2,X3 be a random sample of size n=3 from...Ch. 5.3 - Prob. 13ECh. 5.3 - Let X1,X2,X3 be independent random variables that...Ch. 5.3 - In considering medical insurance for a certain...Ch. 5.3 - The lifetime in months of a certain part has a...Ch. 5.3 - Two components operate in parallel in a device, so...Ch. 5.3 - Prob. 18ECh. 5.3 - Flip n=8 fair coins and remove all that came up...Ch. 5.3 - Prob. 20ECh. 5.4 - Let X1+X2+X3 be a random sample of size 3 from the...Ch. 5.4 - Let X1 and X2 have independent distributions...Ch. 5.4 - Prob. 3ECh. 5.4 - Generalize Exercise 5.4-3 by showing that the sum...Ch. 5.4 - Let Z1,Z2,....,Z7 be a random sample from the...Ch. 5.4 - Let X1,X2,X3,X4,X5 be a random sample of size 5...Ch. 5.4 - Let X1,X2,X3 denote a random sample of size 3 from...Ch. 5.4 - Let W=X1+X2+...+Xh, a sum of h mutually...Ch. 5.4 - Let X and Y, with respective pmfs f(x) and g(y),...Ch. 5.4 - Let X equal the outcome when a fair four-sided die...Ch. 5.4 - Let X and Y equal the outcomes when two fair...Ch. 5.4 - Let X and Y be the outcomes when a pair of fair...Ch. 5.4 - Let X1,X2,...,X8 be a random sample from a...Ch. 5.4 - The number of accidents in a period of one week...Ch. 5.4 - Given a fair four-sided die, let Y equal the...Ch. 5.4 - The number X of sick days taken during a year by...Ch. 5.4 - In a study concerning a new treatment of a certain...Ch. 5.4 - The number of cracks on a highway averages 0.5 per...Ch. 5.4 - A doorman at a hotel is trying to get three taxic...Ch. 5.4 - The time X in minutes of a visit to a...Ch. 5.4 - Let X and Y be independent with distributions...Ch. 5.4 - Let X1 and X2 be two independent random variables....Ch. 5.4 - Let X be N(0,1). Use the mgf technique to show...Ch. 5.4 - Let X1,X2,X3,X4 be a random sample from a x2(r)...Ch. 5.5 - Let X1,X2...,X16, be a random sample from a normal...Ch. 5.5 - Let X be N(50,36). Using the same set of axes,...Ch. 5.5 - Let X equal the widest diameter (in millimeters)...Ch. 5.5 - Let X equal the weight of the soap in a 6-pound...Ch. 5.5 - Let X equal the weight (in grams) of a nail of the...Ch. 5.5 - Let X1,X2,...,X100 be a random sample from N(,4),...Ch. 5.5 - Suppose that the distribution of the weight of a...Ch. 5.5 - Let X denote the wing length in millimeters of a...Ch. 5.5 - Suppose that the length of life in hours (say, X)...Ch. 5.5 - A consumer buys n light bulbs, each of which has a...Ch. 5.5 - A marketing research firm suggests to a comp any...Ch. 5.5 - Let the independent random variables X1 and X2 be...Ch. 5.5 - Prob. 13ECh. 5.5 - Let T have at distribution with r degrees of freed...Ch. 5.5 - Let the distribution of T be t(17). Find (a)...Ch. 5.5 - Prob. 16ECh. 5.6 - Let X be the mean of a random sample of size 12...Ch. 5.6 - Let Y=X1+X2+....+X15 be the sum of a random sample...Ch. 5.6 - Let X be the mean of a random sample of size 36...Ch. 5.6 - Approximate P(39.75X41.25), where X is the mean of...Ch. 5.6 - Let X1,X2,...,X18 be a random sample of size 18...Ch. 5.6 - A random sample of size ii = 18 is taken from the...Ch. 5.6 - Let X equal the maximal oxygen intake of a human...Ch. 5.6 - Let X equal the weight in grams of a miniature...Ch. 5.6 - In Example 5.6-4, with n=4, compute P(1.73.2) and...Ch. 5.6 - Prob. 10ECh. 5.6 - The tensile strength X of paper, in pounds per...Ch. 5.6 - At certain times during the year, a bus company...Ch. 5.6 - Prob. 13ECh. 5.6 - Suppose that the sick leave taken by the typical...Ch. 5.7 - Let the distribution of Y be b(25,1/2). Find the...Ch. 5.7 - Suppose that among gifted seventh-graders who...Ch. 5.7 - A public opinion poll in Southern California was...Ch. 5.7 - Let X equal the number out of n=48 mature aster...Ch. 5.7 - Let X1,X2,...,X48 be a random sample of size 48...Ch. 5.7 - In adults, the pneumococcus bacterium causes 70%...Ch. 5.7 - Let X equal the number of alpha particles emitted...Ch. 5.7 - A candy maker produces mints that have a label...Ch. 5.7 - Let X1,X2,...,X30 be a random sample of size 30...Ch. 5.7 - Prob. 10ECh. 5.7 - On January 1 of a given year, a college basketball...Ch. 5.7 - If X is b(100,0.1), find the approximate value of...Ch. 5.7 - Let X1,X2,...,X36 be a random sample of size 36...Ch. 5.7 - A die is rolled 24 independent times. Let V be the...Ch. 5.7 - In the United States, the probability that a child...Ch. 5.7 - Let X equal the sum of n=100 Bernoulli trials....Ch. 5.7 - The number of trees in one acre has a Poisson...Ch. 5.7 - Assume that the background noise X of a digital...Ch. 5.7 - A company has a one-year group life policy that...Ch. 5.8 - If X is a random variable with mean 33 and...Ch. 5.8 - If E(X)=17 and E(X2)=298, use Chebyshevs...Ch. 5.8 - Let X denote the outcome when a fair die is...Ch. 5.8 - If Y is b(n,0.5), give a lower bound for...Ch. 5.8 - If the distribution of Y is b(n,0.25), give a...Ch. 5.8 - Let X be the mean of a random sample of size n=15...Ch. 5.8 - Suppose that W is a continuous random variable...Ch. 5.9 - Let Y be the number of defectives in a box of 50...Ch. 5.9 - The probability that a certain type of inoculation...Ch. 5.9 - Let S2 be the sample variance of a random sample...Ch. 5.9 - Let Y be x2(n). Use the central limit theorem to...Ch. 5.9 - Let Y have a Poisson distribution with mean 3n....
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Similar questions
- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardPlanetary Velocity The following table gives the mean velocity of planets in their orbits versus their mean distance from the sun. Note that 1AU astronomical unit is the mean distance from Earth to the sun, abut 93 million miles. Planet d=distance AU v=velocity km/sec Mercury 0.39 47.4 Venus 0.72 35.0 Earth 1.00 29.8 Mars 1.52 24.1 Jupiter 5.20 13.1 Saturn 9.58 9.7 Uranus 19.20 6.8 Neptune 30.05 5.4 Astronomers tell us that it is reasonable to model these data with a power function. a Use power regression to express velocity as a power function of distance from the sun. b Plot the data along with the regression equation. c An asteroid orbits at a mean distance of 3AU from the sun. According to the power model you found in part a, what is the mean orbital velocity of the asteroid?arrow_forwardOlympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Statistics 4.1 Point Estimators; Author: Dr. Jack L. Jackson II;https://www.youtube.com/watch?v=2MrI0J8XCEE;License: Standard YouTube License, CC-BY
Statistics 101: Point Estimators; Author: Brandon Foltz;https://www.youtube.com/watch?v=4v41z3HwLaM;License: Standard YouTube License, CC-BY
Central limit theorem; Author: 365 Data Science;https://www.youtube.com/watch?v=b5xQmk9veZ4;License: Standard YouTube License, CC-BY
Point Estimate Definition & Example; Author: Prof. Essa;https://www.youtube.com/watch?v=OTVwtvQmSn0;License: Standard Youtube License
Point Estimation; Author: Vamsidhar Ambatipudi;https://www.youtube.com/watch?v=flqhlM2bZWc;License: Standard Youtube License