 6.6.1: Let Y be a random variable with probability density function given ...
 6.6.2: Let Y be a random variable with a density function given by f (y) =...
 6.6.3: A supplier of kerosene has a weekly demand Y possessing a probabili...
 6.6.4: The amount of flour used per day by a bakery is a random variable Y...
 6.6.5: The waiting time Y until delivery of a new component for an industr...
 6.6.6: The joint distribution of amount of pollutant emitted from a smokes...
 6.6.7: Suppose that Z has a standard normal distribution. a Find the densi...
 6.6.8: Assume that Y has a beta distribution with parameters and . a Find ...
 6.6.9: Suppose that a unit of mineral ore contains a proportion Y1 of meta...
 6.6.11: Suppose that two electronic components in the guidance system for a...
 6.6.12: Suppose that Y has a gamma distribution with parameters and and tha...
 6.6.13: If Y1 and Y2 are independent exponential random variables, both wit...
 6.6.14: In a process of sintering (heating) two types of copper powder (see...
 6.6.15: Let Y have a distribution function given by F(y) = $ 0, y < 0, 1 ey...
 6.6.16: In Exercise 4.15, we determined that f (y) = b y2 , y b, 0, elsewhe...
 6.6.17: A member of the power family of distributions has a distribution fu...
 6.6.18: A member of the Pareto family of distributions (often used in econo...
 6.6.19: Refer to Exercises 6.17 and 6.18. If Y possesses a Pareto distribut...
 6.6.21: Suppose that Y is a random variable that takes on only integer valu...
 6.6.22: Use the results derived in Exercises 4.6 and 6.21 to describe how t...
 6.6.23: In Exercise 6.1, we considered a random variable Y with probability...
 6.6.24: In Exercise 6.4, we considered a random variable Y that possessed a...
 6.6.25: In Exercise 6.4, we considered a random variable Y that possessed a...
 6.6.26: The Weibull density function is given by f (y) = 1 mym1 eym /, y > ...
 6.6.27: Let Y have an exponential distribution with mean . a Prove that W =...
 6.6.28: Let Y have a uniform (0, 1) distribution. Show that U = 2 ln(Y ) ha...
 6.6.29: The speed of a molecule in a uniform gas at equilibrium is a random...
 6.6.31: The joint distribution for the length of life of two different type...
 6.6.32: In Exercise 6.5, we considered a random variable Y that has a unifo...
 6.6.33: The proportion of impurities in certain ore samples is a random var...
 6.6.34: A density function sometimes used by engineers to model lengths of ...
 6.6.35: Let Y1 and Y2 be independent random variables, both uniformly distr...
 6.6.36: Refer to Exercise 6.34. Let Y1 and Y2 be independent Rayleighdistr...
 6.6.37: Let Y1, Y2,..., Yn be independent and identically distributed rando...
 6.6.38: Let Y1 and Y2 be independent random variables with momentgeneratin...
 6.6.39: In Exercises 6.11 and 6.25, we considered two electronic components...
 6.6.41: Let Y1, Y2,..., Yn be independent, normal random variables, each wi...
 6.6.42: A type of elevator has a maximum weight capacity Y1, which is norma...
 6.6.43: Refer to Exercise 6.41. Let Y1, Y2,..., Yn be independent, normal r...
 6.6.44: The weight (in pounds) of mediumsize watermelons is normally distr...
 6.6.45: The manager of a construction job needs to figure prices carefully ...
 6.6.46: Suppose that Y has a gamma distribution with = n/2 for some positiv...
 6.6.47: A random variable Y has a gamma distribution with = 3.5 and = 4.2. ...
 6.6.48: In a missiletesting program, one random variable of interest is th...
 6.6.49: Let Y1 be a binomial random variable with n1 trials and probability...
 6.6.51: Let Y1 be a binomial random variable with n1 trials and p1 = .2 and...
 6.6.52: Let Y1 and Y2 be independent Poisson random variables with means 1 ...
 6.6.53: Let Y1, Y2,..., Yn be independent binomial random variable with ni ...
 6.6.54: Let Y1, Y2,..., Yn be independent Poisson random variables with mea...
 6.6.55: Customers arrive at a department store checkout counter according t...
 6.6.56: The length of time necessary to tune up a car is exponentially dist...
 6.6.57: Let Y1, Y2,..., Yn be independent random variables such that each Y...
 6.6.58: We saw in Exercise 5.159 that the negative binomial random variable...
 6.6.59: Show that if Y1 has a 2 distribution with 1 degrees of freedom and ...
 6.6.61: Refer to Exercise 6.52. Suppose that W = Y1 + Y2 where Y1 and Y2 ar...
 6.6.62: Let Y1 and Y2 be independent normal random variables, each with mea...
 6.6.63: In Example 6.14, Y1 and Y2 were independent exponentially distribut...
 6.6.64: Refer to Exercise 6.63 and Example 6.14. Suppose that Y1 has a gamm...
 6.6.65: Let Z1 and Z2 be independent standard normal random variables and U...
 6.6.66: Let (Y1, Y2) have joint density function fY1,Y2 (y1, y2) and let U1...
 6.6.67: Let (Y1, Y2) have joint density function fY1,Y2 (y1, y2) and let U1...
 6.6.68: Let Y1 and Y2 have joint density function fY1,Y2 (y1, y2) = $ 8y1 y...
 6.6.69: The random variables Y1 and Y2 are independent, both with density f...
 6.6.71: Suppose that Y1 and Y2 are independent exponentially distributed ra...
 6.6.72: Let Y1 and Y2 be independent and uniformly distributed over the int...
 6.6.73: As in Exercise 6.72, let Y1 and Y2 be independent and uniformly dis...
 6.6.74: Let Y1, Y2,..., Yn be independent, uniformly distributed random var...
 6.6.75: Refer to Exercise 6.74. Suppose that the number of minutes that you...
 6.6.76: Let Y1, Y2,..., Yn be independent, uniformly distributed random var...
 6.6.77: Let Y1, Y2,..., Yn be independent, uniformly distributed random var...
 6.6.78: Refer to Exercise 6.76. If Y1, Y2,..., Yn are independent, uniforml...
 6.6.79: Refer to Exercise 6.77. If Y1, Y2,..., Yn are independent, uniforml...
 6.6.81: Let Y1, Y2,..., Yn be independent, exponentially distributed random...
 6.6.82: If Y is a continuous random variable and m is the median of the dis...
 6.6.83: Refer to Exercise 6.82. If Y1, Y2,..., Yn is a random sample from a...
 6.6.84: Refer to Exercise 6.26. The Weibull density function is given by f ...
 6.6.85: Let Y1 and Y2 be independent and uniformly distributed over the int...
 6.6.86: Let Y1, Y2,..., Yn be independent, exponentially distributed random...
 6.6.87: The opening prices per share Y1 and Y2 of two similar stocks are in...
 6.6.88: Suppose that the length of time Y it takes a worker to complete a c...
 6.6.89: Let Y1, Y2,..., Yn denote a random sample from the uniform distribu...
 6.6.91: Suppose that n electronic components, each having an exponentially ...
 6.6.92: If Y1 and Y2 are independent and identically distributed normal ran...
 6.6.93: When current I flows through resistance R, the power generated is g...
 6.6.94: Two efficiency experts take independent measurements Y1 and Y2 on t...
 6.6.95: Let Y1 and Y2 be independent and uniformly distributed over the int...
 6.6.96: Suppose that Y1 is normally distributed with mean 5 and variance 1 ...
 6.6.97: Suppose that Y1 is a binomial random variable with four trials and ...
 6.6.98: The length of time that a machine operates without failure is denot...
 6.6.99: Refer to Exercise 6.98. Show that U, the proportion of time that th...
 6.6.101: A parachutist wants to land at a target T , but she finds that she ...
 6.6.102: Two sentries are sent to patrol a road 1 mile long. The sentries ar...
 6.6.103: Let Y1 and Y2 be independent, standard normal random variables. Fin...
 6.6.104: Let Y1 and Y2 be independent random variables, each having the same...
 6.6.105: A random variable Y has a beta distribution of the second kind, if,...
 6.6.106: If Y is a continuous random variable with distribution function F(y...
 6.6.107: Let Y be uniformly distributed over the interval (1, 3). Find the p...
 6.6.108: If Y denotes the length of life of a component and F(y) is the dist...
 6.6.109: The percentage of alcohol in a certain compound is a random variabl...
 6.6.111: If a random variable U is normally distributed with mean and varian...
 6.6.112: If a random variable U has a gamma distribution with parameters > 0...
 6.6.113: If a random variable U has a gamma distribution with parameters > 0...
 6.6.114: A machine produces spherical containers whose radii vary according ...
 6.6.115: Let v denote the volume of a threedimensional figure. Let Y denote...
 6.6.116: Let (Y1, Y2) have joint density function fY1,Y2 (y1, y2) and let U1...
Solutions for Chapter 6: Functions of Random Variables
Full solutions for Mathematical Statistics with Applications  7th Edition
ISBN: 9780495110811
Solutions for Chapter 6: Functions of Random Variables
Get Full SolutionsChapter 6: Functions of Random Variables includes 105 full stepbystep solutions. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7th. Since 105 problems in chapter 6: Functions of Random Variables have been answered, more than 80638 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).

Backward elimination
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain

Bimodal distribution.
A distribution with two modes

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

Center line
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

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.

Conidence level
Another term for the conidence coeficient.

Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.

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

Control chart
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the incontrol value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be incontrol, or free from assignable causes. Points beyond the control limits indicate an outofcontrol process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

Critical region
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

Critical value(s)
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

Deining relation
A subset of effects in a fractional factorial design that deine the aliases in the design.

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

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.

False alarm
A signal from a control chart when no assignable causes are present

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.

Fraction defective
In statistical quality control, that portion of a number of units or the output of a process that is defective.

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