 4.4.1: The probability distribution of X, the number of imperfections per ...
 4.1E: The current in a certain circuit as measured by an ammeter is a con...
 4.4.2: The probability distribution of the discrete random variable X is f...
 4.2E: Suppose the reaction temperature ?X ?(in ?C) in a certain chemical ...
 4.4.3: Find the mean of the random variable T representing the total of th...
 4.3E: The error involved in making a certain measurement is a continuous ...
 4.4.4: A coin is biased such that a head is three times as likely to occur...
 4.4E: Let ?X ?denote the vibratory stress (psi) on a wind turbine blade a...
 4.4.5: In a gambling game, a woman is paid $3 if she draws a jack or a que...
 4.5E: A college professor never finishes his lecture before the end of th...
 4.4.6: An attendant at a car wash is paid according to the number of cars ...
 4.6E: The actual tracking weight of a stereo cartridge that is set to tra...
 4.4.7: By investing in a particular stock, a person can make a prot in one...
 4.7E: The article ?"Second Moment Reliability Evaluation vs. Monte Carlo ...
 4.4.8: Suppose that an antique jewelry dealer is interested in purchasing ...
 4.8E: In commuting to work, a professor must first get on a bus near her ...
 4.4.9: A private pilot wishes to insure his airplane for $200,000. The ins...
 4.4.10: Two tirequality experts examine stacks of tires and assign a quali...
 4.10E: A family of pdf’s that has been used to approximate the distributio...
 4.4.11: The density function of coded measurements of the pitch diameter of...
 4.11E: Let ?X ?denote the amount of time a book on twohour reserve is act...
 4.12E: The cdf for ? ? = measurement error) of Exercise 3 is a. Compute P(...
 4.4.12: If a dealers prot, in units of $5000, on a new automobile can be lo...
 4.13E: Example 4.5 introduced the concept of time headway in traffic flow ...
 4.4.13: The density function of the continuous random variable X, the total...
 4.14E: The article “Modeling Sediment and Water Column Interactions for Hy...
 4.4.14: Find the proportion X of individuals who can be expected to respond...
 4.15E: Let ? ?denote the amount of space occupied by an article placed in ...
 4.4.15: Assume that two random variables (X,Y ) are uniformly distributed o...
 4.16E: 16E
 4.4.16: Suppose that you are inspecting a lot of 1000 light bulbs, among wh...
 4.17E: 17E
 4.4.17: Let X be a random variable with the following probability distribut...
 4.18E: Let ?X ?denote the voltage at the output of a microphone, and suppo...
 4.4.18: Find the expected value of the random variable g(X)=X2, where X has...
 4.19E: Let ? ?be a continuous rv with cdf [This type of cdf is suggested i...
 4.4.19: A large industrial rm purchases several new word processors at the ...
 4.20E: Consider the pdf for total waiting time Y? ? or two buses introduce...
 4.4.20: A continuous random variable X has the density function f(x)=ex, x ...
 4.21E: An ecologist wishes to mark off a circular sampling region having r...
 4.4.21: What is the dealers average prot per automobile if the prot on each...
 4.22E: The weekly demand for propane gas (in 1000s of gallons) from a part...
 4.4.22: The hospitalization period, in days, for patients following treatme...
 4.23E: If the temperature at which a certain compound melts is a random va...
 4.4.23: Suppose that X and Y have the following joint probability function:...
 4.24E: Let ? h? ave the Pareto pdf introduced in Exercise 10. a.? f k>1, c...
 4.4.24: Referring to the random variables whose joint probability distribut...
 4.25E: Let ?X ?be the temperature in °C at which a certain chemical reacti...
 4.4.25: Referring to the random variables whose joint probability distribut...
 4.26E: Let ?X ?be the total medical expenses (in 1000s of dollars)incurred...
 4.4.26: Let X and Y be random variables with joint density function f(x,y)=...
 4.27E: When a dart is thrown at a circular target, consider the location o...
 4.4.27: In Exercise 3.27 on page 93, a density function is given for the ti...
 4.28E: Let ? ?be a standard normal random variable and calculate the follo...
 4.4.28: Consider the information in Exercise 3.28 on page 93. The problem d...
 4.29E: In each case, determine the value of the constant ?c ?that makes th...
 4.4.29: Exercise 3.29 on page 93 dealt with an important particle size dist...
 4.30E: Find the following percentiles for the standard normal distribution...
 4.4.30: In Exercise 3.31 on page 94, the distribution of times before a maj...
 4.31E: Determine? z?? for the following: a.? = .0055 b.? = .09 c.? = .663
 4.4.31: Consider Exercise 3.32 on page 94. (a) What is the mean proportion ...
 4.32E: Suppose the force acting on a column that helps to support a buildi...
 4.4.32: In Exercise 3.13 on page 92, the distribution of the number of impe...
 4.33E: Mopeds (small motorcycles with an engine capacity below50cm3 ) are ...
 4.4.33: Use Denition 4.3 on page 120 to nd the variance of the random varia...
 4.34E: The article “Reliability of DomesticWaste Biofilm Reactors” (?J. o...
 4.4.34: Let X be a random variable with the following probability distribut...
 4.35E: In a roadpaving process, asphalt mix is delivered to the hopper of...
 4.4.35: The random variable X, representing the number of errors per 100 li...
 4.36E: Spray drift is a constant concern for pesticide applicators and agr...
 4.4.36: Suppose that the probabilities are 0.4, 0.3, 0.2, and 0.1, respecti...
 4.37E: Suppose that blood chloride concentration (mmol/L) has a normal dis...
 4.4.37: A dealers prot, in units of $5000, on a new automobile is a random ...
 4.38E: There are two machines available for cutting corks intended for use...
 4.4.38: The proportion of people who respond to a certain mailorder solici...
 4.39E: The defect length of a corrosion defect in a pressurized steel pipe...
 4.4.39: The total number of hours, in units of 100 hours, that a family run...
 4.40E: The article “Monte Carlo Simulation—Tool for Better Understanding o...
 4.4.40: Referring to Exercise 4.14 on page 117, nd 2 g(X) for the function ...
 4.41E: The automatic opening device of a military cargo parachute has been...
 4.4.41: Find the standard deviation of the random variable g(X) = (2X + 1) ...
 4.42E: The temperature reading from a thermocouple placed in a constantte...
 4.4.42: Using the results of Exercise 4.21 on page 118, nd the variance of ...
 4.43E: Vehicle speed on a particular bridge in China can k modeled as norm...
 4.4.43: The length of time, in minutes, for an airplane to obtain clearance...
 4.44E: If bolt thread length is normally distributed, what is the probabil...
 4.4.44: Find the covariance of the random variables X and Y of Exercise 3.3...
 4.45E: A machine that produces ball bearings has initially been set so tha...
 4.4.45: Find the covariance of the random variables X and Y of Exercise 3.4...
 4.4.46: Find the covariance of the random variables X and Y of Exercise 3.4...
 4.47E: The weight distribution of parcels sent in a certain manner is norm...
 4.4.47: For the random variables X and Y whose joint density function is gi...
 4.48E: Suppose Appendix Table A.3 contained ?(z) only for z ?0 Explain how...
 4.4.48: Given a random variable X, with standard deviation X, and a random ...
 4.49E: Consider babies born in the “normal” range of 37–43 weeks gestation...
 4.4.49: Consider the situation in Exercise 4.32 on page 119. The distributi...
 4.4.50: For a laboratory assignment, if the equipment is working, the densi...
 4.51E: Chebyshev’s inequality, (see Exercise 44, Chapter 3), is valid for ...
 4.4.51: For the random variables X and Y in Exercise 3.39 on page 105, dete...
 4.4.52: Random variables X and Y follow a joint distribution f(x,y)=2, 0 <x...
 4.4.53: Referring to Exercise 4.35 on page 127, nd the mean and variance of...
 4.4.54: Using Theorem 4.5 and Corollary 4.6, nd the mean and variance of th...
 4.4.55: Suppose that a grocery store purchases 5 cartons of skim milk at th...
 4.4.56: Repeat Exercise 4.43 on page 127 by applying Theorem 4.5 and Coroll...
 4.57E: a.? ?Show that if ?X ?has a normal distribution with parameters ? a...
 4.4.57: Let X be a random variable with the following probability distribut...
 4.4.58: The total time, measured in units of 100 hours, that a teenager run...
 4.4.59: If a random variable X is dened such that E[(X 1)2] = 10 and E[(X 2...
 4.4.60: Suppose that X and Y are independent random variables having the jo...
 4.4.61: Use Theorem 4.7 to evaluate E(2XY2 X2Y ) for the joint probability ...
 4.4.62: If X and Y are independent random variables with variances 2 X = 5 ...
 4.4.63: Repeat Exercise 4.62 if X and Y are not independent and XY = 1.
 4.4.64: Suppose that X and Y are independent random variables with probabil...
 4.65E: Let X denote the data transfer time(ms) in a grid computing system ...
 4.4.65: Let X represent the number that occurs when a red die is tossed and...
 4.4.66: Let X represent the number that occurs when a green die is tossed a...
 4.4.67: If the joint density function of X and Y is given by f(x,y)=2 7(x +...
 4.4.68: The power P in watts which is dissipated in an electric circuit wit...
 4.4.69: Consider Review Exercise 3.77 on page 108. The random variables X a...
 4.70E: If ?X ?has an exponential distribution with parameter , derive a ge...
 4.4.70: Consider Review Exercise 3.64 on page 107. There are two service li...
 4.4.71: The length of time Y , in minutes, required to generate a human ree...
 4.72E: The lifetime ?X ?(in hundreds of hours) of a certain type of vacuum...
 4.4.72: A manufacturing company has developed a machine for cleaning carpet...
 4.4.73: For the situation in Exercise 4.72, compute E(eY ) using Theorem 4....
 4.4.74: Consider again the situation of Exercise 4.72. It is required to nd...
 4.75E: Let ?X ?have a Weibull distribution with the pdf from Expression (4...
 4.4.75: An electrical rm manufactures a 100watt light bulb, which, accordi...
 4.4.76: Seventy new jobs are opening up at an automobile manufacturing plan...
 4.4.77: A random variable X has a mean = 10 and a variance 2 = 4. Using Che...
 4.4.78: Compute P( 2<X<+2), where X has the density function f(x)=6x(1x), 0...
 4.4.79: Prove Chebyshevs theorem.
 4.80E: a.? se Equation (4.13) to write a formula for the median of the log...
 4.4.80: Find the covariance of random variables X and Y having the joint pr...
 4.4.81: Referring to the random variables whose joint probability density f...
 4.4.82: Assume the length X, in minutes, of a particular type of telephone ...
 4.4.83: Referring to the random variables whose joint density function is g...
 4.4.84: Referring to the random variables whose joint probability density f...
 4.4.85: Suppose it is known that the life X of a particular compressor, in ...
 4.86E: Stress is applied to a 20in. steel bar that is clamped in a fixed ...
 4.4.86: Referring to the random variables whose joint density function is g...
 4.4.87: Show that Cov(aX,bY )=ab Cov(X,Y ).
 4.4.88: Consider the density function of Review Exercise 4.85. Demonstrate ...
 4.4.89: Consider the joint density function f(x,y)=16y x3 , x > 2, 0 <y<1, ...
 4.4.90: Consider random variables X and Y of Exercise 4.63 on page 138. Com...
 4.4.91: A dealers prot, in units of $5000, on a new automobile is a random ...
 4.4.92: Consider Exercise 4.10 on page 117. Can it be said that the ratings...
 4.4.93: A companys marketing and accounting departments have determined tha...
 4.94E: The accompanying observations are precipitation values during March...
 4.4.94: In a support system in the U.S. space program, a single crucial com...
 4.4.95: In business, it is important to plan and carry out research in orde...
 4.4.96: It is known through data collection and considerable research that ...
 4.4.97: A delivery truck travels from point A to point B and back using the...
 4.4.98: A convenience store has two separate locations where customers can ...
 4.4.99: Consider a ferry that can carry both buses and cars across a waterw...
 4.4.100: As we shall illustrate in Chapter 12, statistical methods associate...
 4.4.101: Consider Review Exercise 3.73 on page 108. It involved Y , the prop...
 4.4.102: Project: Let X = number of hours each student in the class slept th...
 4.117E: Let Z have a standard normal distribution and define a new rv ?Y ?b...
Solutions for Chapter 4: Probability and Statistics for Engineers and the Scientists 9th Edition
Full solutions for Probability and Statistics for Engineers and the Scientists  9th Edition
ISBN: 9780321629111
Solutions for Chapter 4
Get Full SolutionsChapter 4 includes 159 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. Since 159 problems in chapter 4 have been answered, more than 200006 students have viewed full stepbystep solutions from this chapter.

`error (or `risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

Addition rule
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

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.

Assignable cause
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

Biased estimator
Unbiased estimator.

Bivariate normal distribution
The joint distribution of two normal random variables

Causeandeffect diagram
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

Conditional probability
The probability of an event given that the random experiment produces an outcome in another event.

Conidence level
Another term for the conidence coeficient.

Cook’s distance
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

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 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.

Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

Density function
Another name for a probability density function

Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.

Empirical model
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

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.

Gaussian distribution
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

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 .