Solutions for Chapter 3: Discrete Probability Distributions

In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

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.

See Arithmetic mean.

A distribution with two modes

The joint probability distribution of two 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.

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

The probability density function of the conditional probability distribution of a continuous random variable.

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

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

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 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 .

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

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

A quality tool that graphically shows the location of defects on a part or in a process.

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

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

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

Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

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