Advanced Engineering Mathematics 5th Edition - Solutions by Chapter

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

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

The joint distribution of two normal random variables

An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.

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 second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.

The mean of the conditional probability distribution of a random variable.

The probability of an event given that the random experiment produces an outcome in another event.

A probability distribution for a continuous random variable.

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.

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.

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

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

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

The amount of variability exhibited by data

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).

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

The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.

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 .