 3.1E: A concrete beam may fail either by shear (S) or flexure (F). Suppos...
 3.3.1: Classify the following random variables as discrete or continuous: ...
 3.2E: Give three examples of Bernoulli rv’s (other than those in the text).
 3.3.2: An overseas shipment of 5 foreign automobiles contains 2 that have ...
 3.3E: Using the experiment in Example 3.3, define two more random variabl...
 3.3.3: Let W be a random variable giving the number of heads minus the num...
 3.4E: Let X = the number of nonzero digits in a randomly selected zip cod...
 3.3.4: A coin is ipped until 3 heads in succession occur. List only those ...
 3.5E: If the sample space will have an infinite set of possible values? I...
 3.3.5: Determine the value c so that each of the following functions can s...
 3.6E: Starting at a fixed time, each car entering an intersection is obse...
 3.3.6: The shelf life, in days, for bottles of a certain prescribed medici...
 3.7E: For each random variable defined here, describe the set of possible...
 3.3.7: The total number of hours, measured in units of 100 hours, that a f...
 3.8E: Each time a component is tested, the trial is a success (S) or fail...
 3.3.8: Find the probability distribution of the random variable W in Exerc...
 3.9E: An individual named Claudius is located at the point 0 in the accom...
 3.3.9: The proportion of people who respond to a certain mailorder solici...
 3.10E: The number of pumps in use at both a sixpump station and a fourpu...
 3.3.10: Find a formula for the probability distribution of the random varia...
 3.11E: Let X be the number of students who show up for a professor's offic...
 3.3.11: A shipment of 7 television sets contains 2 defective sets. A hotel ...
 3.12E: Airlines sometimes overbook flights. Suppose that for a plane with ...
 3.3.12: An investment rm oers its customers municipal bonds that mature aft...
 3.13E: A mailorder computer business has six telephone lines. Let ?X ?den...
 3.3.13: The probability distribution of X, the number of imperfections per ...
 3.14E: A contractor is required by a county planning department to submit ...
 3.3.14: The waiting time, in hours, between successive speeders spotted by ...
 3.15E: Many manufacturers have quality control programs that include inspe...
 3.3.15: Find the cumulative distribution function of the random variable X ...
 3.16E: Some parts of California are particularly earthquakeprone. Suppose...
 3.3.16: Construct a graph of the cumulative distribution function of Exerci...
 3.17E: A new battery’s voltage may be acceptable (A) or unacceptable (U). ...
 3.3.17: A continuous random variable X that can assume values between x = 1...
 3.18E: Two fair sixsided dice are tossed independently. Let M = the maxim...
 3.3.18: A continuous random variable X that can assume values between x = 2...
 3.19E: A library subscribes to two different weekly news magazines, each o...
 3.3.19: For the density function of Exercise 3.17, nd F(x). Use it to evalu...
 3.20E: Three couples and two single individuals have been invited to an in...
 3.3.20: For the density function of Exercise 3.18, nd F(x), and use it to e...
 3.21E: Suppose that you read through this year’s issues of the New York Ti...
 3.3.21: Consider the density function f(x)=kx, 0 <x<1, 0, elsewhere. (a) Ev...
 3.22E: Refer to Exercise 13, and calculate and graph the cdf F(x). Then us...
 3.3.22: Three cards are drawn in succession from a deck without replacement...
 3.23E: 23E
 3.3.23: Find the cumulative distribution function of the random variable W ...
 3.24E: An insurance company offers its policyholders a number of different...
 3.3.24: Find the probability distribution for the number of jazz CDs when 4...
 3.26E: Alvie Singer lives at 0 in the accompanying diagram and has four fr...
 3.3.25: From a box containing 4 dimes and 2 nickels, 3 coins are selected a...
 3.3.26: From a box containing 4 black balls and 2 green balls, 3 balls are ...
 3.27E: After all students have left the classroom, a statistics professor ...
 3.3.27: The time to failure in hours of an important piece of electronic eq...
 3.28E: Show that the cdf F(x) is a nondecreasing function; that is x1 < x2...
 3.3.28: A cereal manufacturer is aware that the weight of the product in th...
 3.29E: The pmf of the amount of memory X (GB) in a purchased flash drive w...
 3.3.29: An important factor in solid missile fuel is the particle size dist...
 3.30E: An individual who has automobile insurance from a certain company i...
 3.3.30: Measurements of scientic systems are always subject to variation, s...
 3.31E: Refer to Exercise 12 and calculate V(Y) and sY. Then determine the ...
 3.3.31: Based on extensive testing, it is determined by the manufacturer of...
 3.32E: 32E
 3.3.32: The proportion of the budget for a certain type of industrial compa...
 3.33E: Let X be a Bernoulli rv with pmf as in Example 3.18. a.? ?Compute E...
 3.3.33: Suppose a certain type of small data processing rm is so specialize...
 3.34E: Suppose that the number of plants of a particular type found in a r...
 3.3.34: Magnetron tubes are produced on an automated assembly line. A sampl...
 3.35E: A small market orders copies of a certain magazine for its magazine...
 3.3.35: Suppose it is known from large amounts of historical data that X, t...
 3.36E: Let X be the damage incurred (in $) in a certain type of accident d...
 3.3.36: On a laboratory assignment, if the equipment is working, the densit...
 3.37E: The n candidates for a job have been ranked 1, 2, 3, . . . , n. Let...
 3.3.37: Determine the values of c so that the following functions represent...
 3.38E: 38E
 3.3.38: If the joint probability distribution of X and Y is given byf(x,y)=...
 3.39E: A chemical supply company currently has in stock 100 lb of a certai...
 3.3.39: From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas,...
 3.40E: a. ?Draw a line graph of the pmf of ?X ?in Exercise 35. Then determ...
 3.3.40: A fastfood restaurant operates both a drivethrough facility and a ...
 3.41E: Use the definition in Expression (3.13) to prove that V(aX + b) = ?...
 3.3.41: A candy company distributes boxes of chocolates with a mixture of c...
 3.42E: Suppose E(X) = 5 E[X(X  1)] = 27.5 What is a.? ?E(X2)? [Hint: E[X(...
 3.3.42: Let X and Y denote the lengths of life, in years, of two components...
 3.43E: Write a general rule for E(X  c) where c is a constant. What happe...
 3.3.43: Let X denote the reaction time, in seconds, to a certain stimulus a...
 3.44E: A result called ?Chebyshev’s inequality ?states that for any probab...
 3.3.44: Each rear tire on an experimental airplane is supposed to be lled t...
 3.45E: If a ? X ? b, show that a ? E(X) ? b.
 3.3.45: Let X denote the diameter of an armored electric cable and Y denote...
 3.46E: Compute the following binomial probabilities directly from the form...
 3.3.46: Referring to Exercise 3.38, nd (a) the marginal distribution of X; ...
 3.47E: The article ?"Should You Report That FenderBender?" (Consumer Repo...
 3.3.47: The amount of kerosene, in thousands of liters, in a tank at the be...
 3.48E: 48E
 3.3.48: Referring to Exercise 3.39, nd (a) f(y2) for all values of y; (b) ...
 3.49E: A company that produces fine crystal knows from experience that 10%...
 3.3.49: Let X denote the number of times a certain numerical control machin...
 3.50E: A particular telephone number is used to receive both voice calls a...
 3.3.50: Suppose that X and Y have the following joint probability distribut...
 3.51E: Refer to the previous exercise. a.? ?What is the expected number of...
 3.3.51: Three cards are drawn without replacement from the 12 face cards (j...
 3.52E: Suppose that 30% of all students who have to buy a text for a parti...
 3.3.52: A coin is tossed twice. Let Z denote the number of heads on the rst...
 3.53E: Exercise 30 (Section 3.3) gave the pmf of ?Y, ?the number of traffi...
 3.3.53: Given the joint density function f(x,y)=6xy 8 , 0 <x<2, 2 <y<4, 0, ...
 3.54E: A particular type of tennis racket comes in a midsize version and a...
 3.3.54: Determine whether the two random variables of Exercise 3.49 are dep...
 3.55E: Twenty percent of all telephones of a certain type are submitted fo...
 3.3.55: Determine whether the two random variables of Exercise 3.50 are dep...
 3.56E: The College Board reports that 2% of the 2 million high school stud...
 3.3.56: The joint density function of the random variables X and Y is f(x,y...
 3.57E: A certain type of flashlight requires two typeD batteries, and the...
 3.3.57: Let X, Y , and Z have the joint probability density function f(x,y,...
 3.58E: A very large batch of components has arrived at a distributor. The ...
 3.3.58: Determine whether the two random variables of Exercise 3.43 are dep...
 3.59E: An ordinance requiring that a smoke detector be installed in all pr...
 3.3.59: Determine whether the two random variables of Exercise 3.44 are dep...
 3.60E: A toll bridge charges $1.00 for passenger cars and $2.50 for other ...
 3.3.60: The joint probability density function of the random variables X, Y...
 3.61E: A student who is trying to write a paper for a course has a choice ...
 3.3.61: A tobacco company produces blends of tobacco, with each blend conta...
 3.62E: a. ?For fixed n, are there values of p (0 ? p ? 1) for which V(X) =...
 3.3.62: An insurance company oers its policyholders a number of dierent pre...
 3.63E: a.? ?Show that b(x; n, 1  p) = b(n  x; n, p). b. ?Show that B(x; ...
 3.3.63: Two electronic components of a missile system work in harmony for t...
 3.64E: Show that E(X) = np when X is a binomial random variable. [Hint: Fi...
 3.3.64: A service facility operates with two service lines. On a randomly s...
 3.65E: Customers at a gas station pay with a credit card (A), debit card (...
 3.3.65: Let the number of phone calls received by a switchboard during a 5...
 3.66E: An airport limousine can accommodate up to four passengers on any o...
 3.3.66: Consider the random variables X and Y with joint density function f...
 3.67E: Refer to Chebyshev’s inequality given in Exercise 44. Calculate P( ...
 3.3.67: An industrial process manufactures items that can be classied as ei...
 3.68E: Eighteen individuals are scheduled to take a driving test at a part...
 3.3.68: Consider the following joint probability density function of the ra...
 3.69E: Each of 12 refrigerators of a certain type has been returned to a d...
 3.3.69: The life span in hours of an electrical component is a random varia...
 3.70E: An instructor who taught two sections of engineering statistics las...
 3.3.70: Pairs of pants are being produced by a particular outlet facility. ...
 3.71E: A geologist has collected 10 specimens of basaltic rock and 10 spec...
 3.3.71: The shelf life of a product is a random variable that is related to...
 3.72E: A personnel director interviewing 11 senior engineers for four job ...
 3.3.72: Passenger congestion is a service problem in airports. Trains are i...
 3.73E: Twenty pairs of individuals playing in a bridge tournament have bee...
 3.3.73: Impurities in a batch of nal product of a chemical process often re...
 3.74E: A secondstage smog alert has been called in a certain area of Los ...
 3.3.74: The time Z in minutes between calls to an electrical supply system ...
 3.75E: The probability that a randomly selected box of a certain type of c...
 3.3.75: A chemical system that results from a chemical reaction has two imp...
 3.76E: A family decides to have children until it has three children of th...
 3.3.76: Consider the situation of Review Exercise 3.75. But suppose the joi...
 3.77E: Three brothers and their wives decide to have children until each f...
 3.3.77: Consider the random variables X and Y that represent the number of ...
 3.78E: According to the article “Characterizing the Severity and Risk of D...
 3.3.78: The behavior of series of components plays a huge role in scientic ...
 3.79E: 79E
 3.3.79: Another type of system that is employed in engineering work is a gr...
 3.80E: Let X be the number of material anomalies occurring in a particular...
 3.3.80: Consider a system of components in which there are 5 independent co...
 3.81E: Suppose that the number of drivers who travel between a particular ...
 3.3.81: Take 5 class periods to observe the shoe color of individuals in cl...
 3.82E: Consider writing onto a computer disk and then sending it through a...
 3.83E: An article in the Los Angeles Times (Dec. 3, 1993) reports that 1 i...
 3.84E: The ?Centers for Disease Control and Prevention reported in 2012 th...
 3.85E: Suppose small aircraft arrive at a certain airport according to a P...
 3.86E: Organisms are present in ballast water discharged from a ship accor...
 3.87E: The number of requests for assistance received by a towing service ...
 3.88E: In proof testing of circuit boards, the probability that any partic...
 3.89E: The article “ReliabilityBased ServiceLife Assessment of Aging Con...
 3.90E: Let X have a Poisson distribution with parameter ?. Show that E( X ...
 3.91E: Suppose that trees are distributed in a forest according to a twod...
 3.92E: Automobiles arrive at a vehicle equipment inspection station accord...
 3.94E: Consider a deck consisting of seven cards, marked 1, 2, . . . , 7. ...
 3.95E: After shuffling a deck of 52 cards, a dealer deals out 5. Let X = t...
 3.96E: The negative binomial rv X was defined as the number of F’s precedi...
 3.97E: Of all customers purchasing automatic garagedoor openers, 75% purc...
 3.98E: 98E
 3.99E: A koutofn system is one that will function if and only if at lea...
 3.100E: A manufacturer of integrated circuit chips wishes to control the qu...
 3.101E: Of the people passing through an airport metal detector, .5% activa...
 3.102E: An educational consulting firm is trying to decide whether high sch...
 3.103E: Consider a disease whose presence can be identified by carrying out...
 3.104E: Let p1 denote the probability that any particular code symbol is er...
 3.105E: The purchaser of a powergenerating unit requires c consecutive suc...
 3.106E: A plan for an executive travelers’ club has been developed by an ai...
 3.107E: Forty percent of seeds from maize (modernday corn) ears carry sing...
 3.108E: A trial has just resulted in a hung jury because eight members of t...
 3.109E: A reservation service employs five information operators who receiv...
 3.110E: Grasshoppers are distributed at random in a large field according t...
 3.111E: A newsstand has ordered five copies of a certain issue of a photogr...
 3.112E: Individuals A and B begin to play a sequence of chess games. Let S ...
 3.113E: A test for the presence of a certain disease has probability .20 of...
 3.114E: The generalized negative binomial pmf is given by Let X, the number...
 3.115E: There are two Certified Public Accountants in a particular office w...
 3.116E: The mode of a discrete random variable X with pmf p(x) is that valu...
 3.117E: A computer disk storage device has ten concentric tracks, numbered ...
 3.118E: If X is a hypergeometric rv, show directly from the definition that...
 3.119E: Use the fact that to prove Chebyshev’s inequality given in Exercise...
 3.120E: The simple Poisson process of Section 3.6 is characterized by a con...
 3.121E: Consider a collection A1, . . . , Ak of mutually exclusive and exha...
 3.122E: Consider a communication source that transmits packets containing d...
Solutions for Chapter 3: Probability and Statistics for Engineering and the Sciences 9th Edition
Full solutions for Probability and Statistics for Engineering and the Sciences  9th Edition
ISBN: 9780321629111
Solutions for Chapter 3
Get Full SolutionsChapter 3 includes 201 full stepbystep solutions. This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences, edition: 9. This expansive textbook survival guide covers the following chapters and their solutions. Probability and Statistics for Engineering and the Sciences was written by and is associated to the ISBN: 9780321629111. Since 201 problems in chapter 3 have been answered, more than 92503 students have viewed full stepbystep solutions from this chapter.

Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

Bayes’ estimator
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.

Bernoulli trials
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

Bivariate distribution
The joint probability distribution of two random variables.

Categorical data
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

Confounding
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.

Contrast
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

Correlation matrix
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the offdiagonal elements rij are the correlations between Xi and Xj .

Covariance
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

Covariance matrix
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the offdiagonal elements are the covariances between Xi and Xj . Also called the variancecovariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.

Deming
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

Expected value
The expected value of a random variable X is its longterm average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

Exponential random variable
A series of tests in which changes are made to the system under study

Forward selection
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

Hat matrix.
In multiple regression, the matrix H XXX X = ( ) ? ? 1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .