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.

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

An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

The joint probability distribution of two random variables.

A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

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 square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .

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

Another name for a cumulative distribution function.

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

A subset of a sample space.

A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.

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.

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

The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .