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# Solutions for Chapter 6.2: Transforming and Combining Random Variables

## Full solutions for The Practice of Statistics | 5th Edition

ISBN: 9781464108730

Solutions for Chapter 6.2: Transforming and Combining Random Variables

Solutions for Chapter 6.2
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##### ISBN: 9781464108730

Since 34 problems in chapter 6.2: Transforming and Combining Random Variables have been answered, more than 25103 students have viewed full step-by-step solutions from this chapter. Chapter 6.2: Transforming and Combining Random Variables includes 34 full step-by-step solutions. The Practice of Statistics was written by and is associated to the ISBN: 9781464108730. This textbook survival guide was created for the textbook: The Practice of Statistics, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions.

Key Statistics Terms and definitions covered in this textbook
• Alias

In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Analysis of variance (ANOVA)

A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

• 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.

• Bivariate normal distribution

The joint distribution of two normal random variables

• Chance cause

The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

• Conditional mean

The mean of the conditional probability distribution of a random variable.

• Continuous uniform random variable

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

• 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 off-diagonal 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 .

• 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.

• Deining relation

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

• Dispersion

The amount of variability exhibited by data

• Error mean square

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

• Error propagation

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

• Estimate (or point estimate)

The numerical value of a point estimator.

• Estimator (or point estimator)

A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

• Exhaustive

A property of a collection of events that indicates that their union equals the sample space.

• F distribution.

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

• First-order model

A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model

• Generating function

A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function

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