Advanced Engineering Mathematics 5th Edition - Solutions by Chapter

In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.

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

A set of rules that probabilities deined on a sample space must follow. See Probability

In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

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.

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

When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

A subset of effects in a fractional factorial design that deine the aliases in the design.

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

Another name for a probability density function

The response variable in regression or a designed experiment.

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 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 method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

A function used in the probability density function of a gamma random variable that can be considered to extend factorials

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

A discrete random variable that is the number of Bernoulli trials until a success occurs.

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 .