Probability and Statistics with Reliability, Queuing, and Computer Science Applications 2nd 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).

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

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.

In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

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

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

A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

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

A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

A random variable with an interval (either inite or ininite) of real numbers for its range.

In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

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 .

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

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

A signal from a control chart when no assignable causes are present

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

A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

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 .