 5.1E: Contracts for two construction jobs are randomly assigned to one or...
 5.2E: Three balanced coins are tossed independently. One of the variables...
 5.3E: Of nine executives in a business firm, four are married, three have...
 5.4E: Given here is the joint probability function associated with data o...
 5.5E: Refer to Example 5.4. The joint density of Y1, the proportion of th...
 5.6E: Refer to Example 5.3. If a radioactive particle is randomly located...
 5.7E: Let Y1 and Y2 have joint density function a What is P(Y1 < 1, Y2 > ...
 5.8E: Let Y1 and Y2 have the joint probability density function given by ...
 5.9E: Let Y1 and Y2 have the joint probability density function given by ...
 5.10E: An environmental engineer measures the amount (by weight) of partic...
 5.11E: Suppose that Y1 and Y2 are uniformly distributed over the triangle ...
 5.12E: Let Y1 and Y2 denote the proportions of two different types of comp...
 5.13E: The joint density function of Y1 and Y2 is given by
 5.144SE: Prove Theorem 5.9 when Y1 and Y2 are independent discrete random va...
 5.14E: Suppose that the random variables Y1 and Y2 have joint probability ...
 5.15E: The management at a fastfood outlet is interested in the joint beh...
 5.16E: Let Y1 and Y2 denote the proportions of time (out of one workday) d...
 5.17E: Let (Y1, Y2) denote the coordinates of a point chosen at random ins...
 5.18E: An electronic system has one each of two different types of compone...
 5.19E: In Exercise 5.1, we determined that the joint distribution of Y1, t...
 5.20E: Refer to Exercise 5.2.a Derive the marginal probability distributio...
 5.21E: In Exercise 5.3, we determined that the joint probability distribut...
 5.22E: In Exercise 5.4, you were given the following joint probability fun...
 5.23E: In Example 5.4 and Exercise 5.5, we considered the joint density of...
 5.24E: In Exercise 5.6, we assumed that if a radioactive particle is rando...
 5.25E: Let Y1 and Y2 have joint density function first encountered in Exer...
 5.26E: In Exercise 5.8, we derived the fact that is a valid joint probabil...
 5.27E: In Exercise 5.9, we determined that is a valid joint probability de...
 5.28E: In Exercise 5.10, we proved that is a valid joint probability densi...
 5.29E: Refer to Exercise 5.11. Finda the marginal density functions for Y1...
 5.30E: In Exercise 5.12, we were given the following joint probability den...
 5.31E: In Exercise 5.13, the joint density function of Y1 and Y2 is given ...
 5.32E: Suppose that the random variables Y1 and Y2 have joint probability ...
 5.33E: Suppose that Y1 is the total time between a customer’s arrival in t...
 5.34E: If Y1 is uniformly distributed on the interval (0, 1) and, for 0 < ...
 5.35E: Refer to Exercise 5.33. If two minutes elapse between a customer’s ...
 5.36E: In Exercise 5.16, Y1 and Y2 denoted the proportions of time during ...
 5.37E: In Exercise 5.18, Y1 and Y2 denoted the lengths of life, in hundred...
 5.38E: Let Y1 denote the weight (in tons) of a bulk item stocked by a supp...
 5.39E: Suppose that Y1 and Y2 are independent Poisson distributed random v...
 5.40E: Suppose that Y1 and Y2 are independent binomial distributed random ...
 5.41E: A quality control plan calls for randomly selecting three items fro...
 5.42E: The number of defects per yard Y for a certain fabric is known to h...
 5.43E: Let Y1 and Y2 have joint density function f (y1, y2) and marginal d...
 5.44E: Prove that the results in Exercise 5.43 also hold for discrete rand...
 5.45E: In Exercise 5.1, we determined that the joint distribution of Y1, t...
 5.46E: Refer to Exercise 5.2. The number of heads in three coin tosses is ...
 5.47E: In Exercise 5.3, we determined that the joint probability distribut...
 5.48E: In Exercise 5.4, you were given the following joint probability fun...
 5.49E: In Example 5.4 and Exercise 5.5, we considered the joint density of...
 5.50E: In Exercise 5.6, we assumed that if a radioactive particle is rando...
 5.51E: In Exercise 5.7, we considered Y1 and Y2 with joint density functio...
 5.52E: In Exercise 5.8, we derived the fact that is a valid joint probabil...
 5.53E: In Exercise 5.9, we determined that is a valid joint probability de...
 5.54E: In Exercise 5.10, we proved that is a valid joint probability densi...
 5.55E: Suppose that, as in Exercise 5.11, Y1 and Y2 are uniformly distribu...
 5.56E: In Exercise 5.12, we were given the following joint probability den...
 5.57E: In Exercises 5.13 and 5.31, the joint density function of Y1 and Y2...
 5.58E: Suppose that the random variables Y1 and Y2 have joint probability ...
 5.59E: Exercise 5.32 Suppose that the random variables Y1 and Y2 have join...
 5.60E: In Exercise 5.16, Y1 and Y2 denoted the proportions of time that em...
 5.61E: In Exercise 5.18, Y1 and Y2 denoted the lengths of life, in hundred...
 5.62E: Suppose that the probability that a head appears when a coin is tos...
 5.63E: Let Y1 and Y2 be independent exponentially distributed random varia...
 5.64E: Let Y1 and Y2 be independent random variables that are both uniform...
 5.65E: Suppose that, for ?1 ? ? ? 1, the probability density function of (...
 5.66E: Let F1(y1) and F2(y2) be two distribution functions. For any ?, ?1 ...
 5.67E: In Section 5.2, we argued that if Y1 and Y2 have joint cumulative d...
 5.68E: A supermarket has two customers waiting to pay for their purchases ...
 5.69E: The length of life Y for fuses of a certain type is modeled by the ...
 5.70E: A bus arrives at a bus stop at a uniformly distributed time over th...
 5.71E: Two telephone calls come into a switchboard at random times in a fi...
 5.72E: In Exercise 5.1, we determined that the joint distribution of Y1, t...
 5.73E: In Exercise 5.3, we determined that the joint probability distribut...
 5.74E: Refer to Exercises 5.6, 5.24, and 5.50. Suppose that a radioactive ...
 5.75E: Refer to Exercises 5.7, 5.25, and 5.51. Let Y1 and Y2 have joint de...
 5.76E: In Exercise 5.8, we derived the fact that ReferenceLet Y1 and Y2 ha...
 5.77E: In Exercise 5.9, we determined that ReferenceLet Y1 and Y2 have the...
 5.78E: In Exercise 5.10, we proved that is a valid joint probability densi...
 5.79E: Suppose that, as in Exercise 5.11, Y1 and Y2 are uniformly distribu...
 5.80E: In Exercise 5.16, Y1 and Y2 denoted the proportions of time that em...
 5.81E: In Exercise 5.18, Y1 and Y2 denoted the lengths of life, in hundred...
 5.82E: In Exercise 5.38, we determined that the joint density function for...
 5.83E: In Exercise 5.42, we determined that the unconditional probability ...
 5.84E: In Exercise 5.62, we considered two individuals who each tossed a c...
 5.85E: In Exercise 5.65, we considered random variables Y1 and Y2 that, fo...
 5.86E: Suppose that Z is a standard normal random variable and that Y1 and...
 5.87E: Suppose that Y1 and Y2 are independent ? 2 random variables with ?1...
 5.88E: Suppose that you are told to toss a die until you have observed eac...
 5.89E: In Exercise 5.1, we determined that the joint distribution of Y1, t...
 5.90E: In Exercise 5.3, we determined that the joint probability distribut...
 5.91E: In Exercise 5.8, we derived the fact that ReferenceLet Y1 and Y2 ha...
 5.92E: In Exercise 5.9, we determined that ReferenceLet Y1 and Y2 have the...
 5.93E: Suppose that, as in Exercises 5.11 and 5.79, Y1 and Y2 are uniforml...
 5.94E: Let Y1 and Y2 be uncorrelated random variables and consider U1 = Y1...
 5.95E: Let the discrete random variables Y1 and Y2 have the joint probabil...
 5.96E: Suppose that the random variables Y1 and Y2 have means ?1 and ?2 an...
 5.97E: The random variables Y1 and Y2 are such that E(Y1) = 4, E(Y2) = ?1,...
 5.98E: How big or small can Cov(Y1, Y2) be? Use the fact that ?2 ? 1 to sh...
 5.99E: If c is any constant and Y is a random variable such that E(Y ) exi...
 5.100E: Let Z be a standard normal random variable and let Y1 = Z and Y2 = ...
 5.101E: In Exercise 5.65, we considered random variables Y1 and Y2 that, fo...
 5.102E: A firm purchases two types of industrial chemicals. Type I chemical...
 5.103E: Assume that Y1, Y2, and Y3 are random variables, with
 5.104E: In Exercise 5.3, we determined that the joint probability distribut...
 5.105E: In Exercise 5.8, we established that is a valid joint probability d...
 5.106E: In Exercise 5.9, we determined that ReferenceLet Y1 and Y2 have the...
 5.107E: In Exercise 5.12, we were given the following joint probability den...
 5.108E: If Y1 is the total time between a customer’s arrival in the store a...
 5.109E: In Exercise 5.16, Y1 and Y2 denoted the proportions of time that em...
 5.110E: Suppose that Y1 and Y2 have correlation coefficient ? = .2. What is...
 5.111E: Suppose that Y1 and Y2 have correlation coefficient ?Y1 ,Y2 and for...
 5.112E: In Exercise 5.18, Y1 and Y2 denoted the lengths of life, in hundred...
 5.113E: A retail grocery merchant figures that her daily gain X from sales ...
 5.114E: For the daily output of an industrial operation, let Y1 denote the ...
 5.115E: Refer to Exercise 5.88. If Y denotes the number of tosses of the di...
 5.116E: Refer to Exercise 5.75. Use Theorem 5.12 to explain why V (Y1 + Y2)...
 5.117E: A population of N alligators is to be sampled in order to obtain an...
 5.118E: The total sustained load on the concrete footing of a planned build...
 5.119E: A learning experiment requires a rat to run a maze (a network of pa...
 5.120E: A sample of size n is selected from a large lot of items in which a...
 5.121E: Refer to Exercise 5.117. Suppose that the number N of alligators in...
 5.122E: The weights of a population of mice fed on a certain diet since bir...
 5.123E: The National Fire Incident Reporting Service stated that, among res...
 5.124E: The typical cost of damages caused by a fire in a family home is $2...
 5.125E: When commercial aircraft are inspected, wing cracks are reported as...
 5.126E: A large lot of manufactured items contains 10% with exactly one def...
 5.127E: Refer to Exercise 5.126. Let Y denote the number of items among the...
 5.128E: Let Y1 and Y2 have a bivariate normal distribution.a Show that the ...
 5.129E: Let Y1 and Y2 have a bivariate normal distribution. Show that the c...
 5.130E: Let Y1, Y2, . . . , Yn be independent random variables with E(Yi ) ...
 5.131E: Let Y1 and Y2 be independent normally distributed random variables ...
 5.132E: Refer to Exercise 5.131. What are the marginal distributions of U1 ...
 5.133E: In Exercise 5.9, we determined that is a valid joint probability de...
 5.134E: In Examples 5.32 and 5.33, we determined that if Y is the number of...
 5.135E: In Exercise 5.41, we considered a quality control plan that calls f...
 5.136E: In Exercise 5.42, the number of defects per yard in a certain fabri...
 5.137E: In Exercise 5.38, we assumed that Y1, the weight of a bulk item sto...
 5.138E: Assume that Y denotes the number of bacteria per cubic centimeter i...
 5.139E: Suppose that a company has determined that the the number of jobs p...
 5.140E: Why is E[V (Y1Y2)] ? V (Y1)?
 5.141E: Let Y1 have an exponential distribution with mean ? and the conditi...
 5.142E: Suppose that Y has a binomial distribution with parameters n and p ...
 5.143E: If Y1 and Y2 are independent random variables, each having a normal...
 5.145SE: A technician starts a job at a time Y1 that is uniformly distribute...
 5.146SE: A target for a bomb is in the center of a circle with radius of 1 m...
 5.147SE: Two friends are to meet at the library. Each independently and rand...
 5.148SE: A committee of three people is to be randomly selected from a group...
 5.149SE: Let Y1 and Y2 have a joint density function given by a Find the mar...
 5.150SE: Refer to Exercise 5.149.a Find E(Y2Y1 = y1).b Use Theorem 5.14 to ...
 5.151SE: The lengths of life Y for a type of fuse has an exponential distrib...
 5.152SE: ?. In the production of a certain type of copper, two types of copp...
 5.153SE: Suppose that the number of eggs laid by a certain insect has a Pois...
 5.154SE: In a clinical study of a new drug formulated to reduce the effects ...
 5.155SE: Suppose that Y1, Y2, and Y3 are independent ? 2distributed random ...
 5.156SE: Refer to Exercise 5.86. Suppose that Z is a standard normal random ...
 5.157SE: A forester studying diseased pine trees models the number of diseas...
 5.158SE: A coin has probability p of coming up heads when tossed. In n indep...
 5.159SE: The negative binomial random variable Y was defined in Section 3.6 ...
 5.160SE: A box contains four balls, numbered 1 through 4. One ball is select...
 5.161SE: Suppose that we are to observe two independent random samples: Y1, ...
 5.162SE: In Exercise 5.65, you determined that, for ?1 ? ? ? 1, the probabil...
 5.163SE: Refer to Exercise 5.66. If F1(y1) and F2(y2) are two distribution f...
 5.164SE: Let X1, X2, and X3 be random variables, either continuous or discre...
 5.165SE: Let X1, X2, and X3 have a multinomial distribution with probability...
 5.166SE: A box contains N1 white balls, N2 black balls, and N3 red balls (N1...
 5.167SE: Let Y1 and Y2 be jointly distributed random variables with finite v...
Solutions for Chapter 5: Mathematical Statistics with Applications 7th Edition
Full solutions for Mathematical Statistics with Applications  7th Edition
ISBN: 9780495110811
Solutions for Chapter 5
Get Full SolutionsChapter 5 includes 167 full stepbystep solutions. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. This expansive textbook survival guide covers the following chapters and their solutions. Since 167 problems in chapter 5 have been answered, more than 261198 students have viewed full stepbystep solutions from this chapter. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811.

2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability

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.

Bayes’ theorem
An equation for a conditional probability such as PA B (  ) in terms of the reverse conditional probability PB A (  ).

Biased estimator
Unbiased estimator.

Bivariate distribution
The joint probability distribution of two random variables.

Causal variable
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

Conidence coeficient
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.

Contingency table.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

Continuity correction.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

Continuous distribution
A probability distribution for a continuous random variable.

Convolution
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

Correction factor
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

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 .

Decision interval
A parameter in a tabular CUSUM algorithm that is determined from a tradeoff between false alarms and the detection of assignable causes.

Defect
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

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

Eficiency
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

Enumerative study
A study in which a sample from a population is used to make inference to the population. See Analytic study

Geometric mean.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .