Probability and Statistics for Engineers and Scientists 4th Edition - Solutions by Chapter

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

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.

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

The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

A probability distribution for a continuous random variable.

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

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 .

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.

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

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.

See U chart

The response variable in regression or a designed experiment.

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.

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.

A term in the formula for the variance of a hypergeometric random variable.

A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.

A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

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

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

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 .