 6.1E: Let Y be a random variable with probability density function given by
 6.2E: Let Y be a random variable with a density function given by
 6.3E: A supplier of kerosene has a weekly demand Y possessing a probabili...
 6.4E: The amount of flour used per day by a bakery is a random variable Y...
 6.5E: The waiting time Y until delivery of a new component for an industr...
 6.6E: The joint distribution of amount of pollutant emitted from a smokes...
 6.7E: Suppose that Z has a standard normal distribution.a Find the densit...
 6.8E: Assume that Y has a beta distribution with parameters ? and ?.a Fin...
 6.9E: Suppose that a unit of mineral ore contains a proportion Y1 of meta...
 6.10E: The total time from arrival to completion of service at a fastfood...
 6.11E: Suppose that two electronic components in the guidance system for a...
 6.12E: Suppose that Y has a gamma distribution with parameters ? and ? and...
 6.13E: If Y1 and Y2 are independent exponential random variables, both wit...
 6.14E: In a process of sintering (heating) two types of copper powder (see...
 6.15E: Let Y have a distribution function given by Find a transformation G...
 6.16E: In Exercise 4.15, we determined that is a bona fide probability den...
 6.17E: A member of the power family of distributions has a distribution fu...
 6.18E: A member of the Pareto family of distributions (often used in econo...
 6.19E: Refer to Exercises 6.17 and 6.18. If Y possesses a Pareto distribut...
 6.20E: Let the random variable Y possess a uniform distribution on the int...
 6.21E: Suppose that Y is a random variable that takes on only integer valu...
 6.22E: Use the results derived in Exercises 4.6 and 6.21 to describe how t...
 6.23E: In Exercise 6.1, we considered a random variable Y with probability...
 6.24E: In Exercise 6.4, we considered a random variable Y that possessed a...
 6.25E: In Exercise 6.11, we considered two electronic components that oper...
 6.26E: The Weibull density function is given by where ? and m are positive...
 6.27E: Let Y have an exponential distribution with mean ?.a Prove that W =...
 6.28E: Let Y have a uniform (0, 1) distribution. Show that U = ?2 ln(Y ) h...
 6.29E: The speed of a molecule in a uniform gas at equilibrium is a random...
 6.30E: A fluctuating electric current I may be considered a uniformly dist...
 6.31E: The joint distribution for the length of life of two different type...
 6.32E: In Exercise 6.5, we considered a random variable Y that has a unifo...
 6.33E: The proportion of impurities in certain ore samples is a random var...
 6.34E: A density function sometimes used by engineers to model lengths of ...
 6.35E: Let Y1 and Y2 be independent random variables, both uniformly distr...
 6.36E: Refer to Exercise 6.34. Let Y1 and Y2 be independent Rayleighdistr...
 6.37E: Let Y1, Y2, . . . , Yn be independent and identically distributed r...
 6.38E: Let Y1 and Y2 be independent random variables with momentgeneratin...
 6.39E: In Exercises 6.11 and 6.25, we considered two electronic components...
 6.40E: Suppose that Y1 and Y2 are independent, standard normal random vari...
 6.41E: Let Y1, Y2, . . . , Yn be independent, normal random variables, eac...
 6.42E: A type of elevator has a maximum weight capacity Y1, which is norma...
 6.43E: Refer to Exercise 6.41. Let Y1, Y2, . . . , Yn be independent, norm...
 6.44E: The weight (in pounds) of “mediumsize” watermelons is normally dis...
 6.45E: The manager of a construction job needs to figure prices carefully ...
 6.46E: Suppose that Y has a gamma distribution with ? = n/2 for some posit...
 6.47E: A random variable Y has a gamma distribution with ? = 3.5 and ? = 4...
 6.48E: In a missiletesting program, one random variable of interest is th...
 6.49E: Let Y1 be a binomial random variable with n1 trials and probability...
 6.50E: Let Y be a binomial random variable with n trials and probability o...
 6.51E: Let Y1 be a binomial random variable with n1 trials and p1 = .2 and...
 6.52E: Let Y1 and Y2 be independent Poisson random variables with means ?1...
 6.53E: Let Y1, Y2, . . . , Yn be independent binomial random variable with...
 6.54E: Let Y1, Y2, . . . , Yn be independent Poisson random variables with...
 6.55E: Customers arrive at a department store checkout counter according t...
 6.56E: The length of time necessary to tune up a car is exponentially dist...
 6.57E: Let Y1, Y2, . . . , Yn be independent random variables such that ea...
 6.58E: We saw in Exercise 5.159 that the negative binomial random variable...
 6.59E: Show that if Y1 has a ? 2 distribution with ?1 degrees of freedom a...
 6.60E: Suppose that W = Y1 + Y2 where Y1 and Y2 are independent. If W has ...
 6.61E: Refer to Exercise 6.52. Suppose that W = Y1 + Y2 where Y1 and Y2 ar...
 6.62E: Let Y1 and Y2 be independent normal random variables, each with mea...
 6.63E: In Example 6.14, Y1 and Y2 were independent exponentially distribut...
 6.64E: Refer to Exercise 6.63 and Example 6.14. Suppose that Y1 has a gamm...
 6.65E: Let Z1 and Z2 be independent standard normal random variables and U...
 6.66E: Let (Y1, Y2) have joint density function fY1 ,Y2 (y1, y2) and let U...
 6.67E:
 6.68E: Let Y1 and Y2 have joint density function a Derive the joint densit...
 6.69E: The random variables Y1 and Y2 are independent, both with density
 6.70E: Suppose that Y1 and Y2 are independent and that both are uniformly ...
 6.71E: Suppose that Y1 and Y2 are independent exponentially distributed ra...
 6.72E: Let Y1 and Y2 be independent and uniformly distributed over the int...
 6.73E: As in Exercise 6.72, let Y1 and Y2 be independent and uniformly dis...
 6.74E: Let Y1, Y2, . . . , Yn be independent, uniformlydistributed random ...
 6.75E: Refer to Exercise 6.74. Suppose that the number of minutes that you...
 6.76E: Let Y1, Y2, . . . , Yn be independent, uniformly istributed random ...
 6.77E: Let Y1, Y2, . . . , Yn be independent, uniformly distributed random...
 6.78E: Refer to Exercise 6.76. If Y1, Y2, . . . , Yn are independent, unif...
 6.79E: Refer to Exercise 6.77. If Y1, Y2, . . . , Yn are independent, unif...
 6.80E: Let Y1, Y2, . . . , Yn be independent random variables, each with a...
 6.81E: Let Y1, Y2, . . . , Yn be independent, exponentially distributed ra...
 6.82E: If Y is a continuous random variable and m is the median of the dis...
 6.83E: Refer to Exercise 6.82. If Y1, Y2, . . . , Yn is a random sample fr...
 6.84E: Refer to Exercise 6.26. The Weibull density function is given by Re...
 6.85E: Let Y1 and Y2 be independent and uniformly distributed over the int...
 6.86E: Let Y1, Y2, . . . , Yn be independent, exponentially distributed ra...
 6.87E: The opening prices per share Y1 and Y2 of two similar stocks are in...
 6.88E: Suppose that the length of time Y it takes a worker to complete a c...
 6.89E: Let Y1, Y2, . . . , Yn denote a random sample from the uniform dist...
 6.90E: Suppose that the number of occurrences of a certain event in time i...
 6.92SE: If Y1 and Y2 are independent and identically distributed normal ran...
 6.93SE: When current I flows through resistance R, the power generated is g...
 6.94SE: Two efficiency experts take independent measurements Y1 and Y2 on t...
 6.95SE: Let Y1 and Y2 be independent and uniformly distributed over the int...
 6.96SE: Suppose that Y1 is normally distributed with mean 5 and variance 1 ...
 6.97SE: Suppose that Y1 is a binomial random variable with four trials and ...
 6.98SE: The length of time that a machine operates without failure is denot...
 6.99SE: Refer to Exercise 6.98. Show that U , the proportion of time that t...
 6.100SE: The time until failure of an electronic device has an exponential d...
 6.101SE: A parachutist wants to land at a target T, but she finds that she i...
 6.102SE: Two sentries are sent to patrol a road 1 mile long. The sentries ar...
 6.103SE: Let Y1 and Y2 be independent, standard normal random variables. Fin...
 6.104SE: Let Y1 and Y2 be independent random variables, each having the same...
 6.105SE: A random variable Y has a beta distribution of the second kind, if,...
 6.106SE: If Y is a continuous random variable with distribution function F(y...
 6.107SE: Let Y be uniformly distributed over the interval (?1, 3). Find the ...
 6.108SE: If Y denotes the length of life of a component and F(y) is the dist...
 6.109SE: The percentage of alcohol in a certain compound is a random variabl...
 6.110SE: An engineer has observed that the gap times between vehicles passin...
 6.111SE: If a random variable U is normally distributed with mean ? and vari...
 6.112SE: If a random variable U has a gamma distribution with parameters ? >...
 6.113SE: Let (Y1, Y2) have joint density function fY1 ,Y2 (y1, y2) and let U...
 6.114SE: A machine produces spherical containers whose radii vary according ...
 6.115SE: Let v denote the volume of a threedimensional figure. Let Y denote...
 6.116SE: Let (Y1, Y2) have joint density function fY1 ,Y2 (y1, y2) and let U...
Solutions for Chapter 6: Mathematical Statistics with Applications 7th Edition
Full solutions for Mathematical Statistics with Applications  7th Edition
ISBN: 9780495110811
Solutions for Chapter 6
Get Full SolutionsChapter 6 includes 115 full stepbystep solutions. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7th. Since 115 problems in chapter 6 have been answered, more than 54687 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Mathematical Statistics with Applications was written by Sieva Kozinsky and is associated to the ISBN: 9780495110811.

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.

Alternative hypothesis
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

Bias
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

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

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.

Comparative experiment
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

Contour plot
A twodimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

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 normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

Designed experiment
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

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

Error mean square
The error sum of squares divided by its number of degrees of freedom.

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.

Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

F distribution.
The distribution of the random variable deined as the ratio of two independent chisquare random variables, each divided by its number of degrees of freedom.

Ftest
Any test of signiicance involving the F distribution. The most common Ftests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.

Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.

Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.
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