Solutions for Chapter 7: Functions of Random Variables
Full solutions for Mathematical Statistics with Applications  8th Edition
ISBN: 9780321807090
Solutions for Chapter 7: Functions of Random Variables
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Addition rule
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

Biased estimator
Unbiased estimator.

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

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

Central tendency
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.

Components of variance
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.

Conidence coeficient
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.

Cook’s distance
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

Counting techniques
Formulas used to determine the number of elements in sample spaces and events.

Decision interval
A parameter in a tabular CUSUM algorithm that is determined from a tradeoff between false alarms and the detection of assignable causes.

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

Dependent variable
The response variable in regression or a designed experiment.

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

Dispersion
The amount of variability exhibited by data

Distribution function
Another name for a cumulative distribution function.

Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

Error mean square
The error sum of squares divided by its number of degrees of freedom.

Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

F distribution.
The distribution of the random variable deined as the ratio of two independent chisquare random variables, each divided by its number of degrees of freedom.

Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.