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

A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

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.

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

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 term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

Formulas used to determine the number of elements in sample spaces and events.

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 .

In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.

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

A probability distribution for a discrete random variable

Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

The variance of an error term or component in a model.

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.

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.

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

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