Probability and Statistics with Reliability, Queuing, and Computer Science Applications 2nd Edition - Solutions by Chapter

If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.

A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

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.

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

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

A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

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

An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

A continuous random variable with range of a inite interval and a constant probability density function.

A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

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.

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

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

The numerical value of a point estimator.

A subset of a sample space.

An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on

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