Applied Statistics and Probability for Engineers 3rd Edition - Solutions by Chapter

In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

Any control chart for a discrete random variable. See Variables control chart.

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.

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

Unbiased estimator.

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

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.

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

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

A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control 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 in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

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 .

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

W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

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

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.

A series of tests in which changes are made to the system under study

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

In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .