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# Solutions for Chapter 4.8: Some Other Continuous Distributions

## Full solutions for Statistics for Engineers and Scientists | 4th Edition

ISBN: 9780073401331

Solutions for Chapter 4.8: Some Other Continuous Distributions

Solutions for Chapter 4.8
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##### ISBN: 9780073401331

This expansive textbook survival guide covers the following chapters and their solutions. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Chapter 4.8: Some Other Continuous Distributions includes 17 full step-by-step solutions. Since 17 problems in chapter 4.8: Some Other Continuous Distributions have been answered, more than 289909 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

Key Statistics Terms and definitions covered in this textbook
• 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

• Average run length, or ARL

The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

• 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.

• 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 probability density function

The probability density function of the conditional probability distribution of a continuous random variable.

• Continuity correction.

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

• Contour plot

A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

• Control limits

See Control chart.

• Correlation coeficient

A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

• 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 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 off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

• Curvilinear regression

An expression sometimes used for nonlinear regression models or polynomial regression models.

• Defects-per-unit control chart

See U chart

• Enumerative study

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

• Factorial experiment

A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

• False alarm

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

• Fraction defective

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

• Gamma function

A function used in the probability density function of a gamma random variable that can be considered to extend factorials

• 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

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