Advanced Engineering Mathematics 5th Edition - Solutions by Chapter

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

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).

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

Unbiased estimator.

The joint probability distribution of two random variables.

A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

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

A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

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.

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

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.

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.

A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

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

A probability distribution for a discrete random variable

A random variable with a inite (or countably ininite) range.

The numerical value of a point estimator.

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

Any test of signiicance involving the F distribution. The most common F-tests 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.

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