Solutions for Chapter 3: Probability Distributions and Probability Densities
Full solutions for Mathematical Statistics with Applications  8th Edition
ISBN: 9780321807090
Solutions for Chapter 3: Probability Distributions and Probability Densities
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`error (or `risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

C chart
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defectsperunit or U chart.

Central composite design (CCD)
A secondorder response surface design in k variables consisting of a twolevel factorial, 2k axial runs, and one or more center points. The twolevel factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a secondorder model.

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.

Conditional probability
The probability of an event given that the random experiment produces an outcome in another event.

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

Contour plot
A twodimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

Control chart
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the incontrol value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be incontrol, or free from assignable causes. Points beyond the control limits indicate an outofcontrol process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

Critical region
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

Distribution function
Another name for a cumulative distribution function.

Eficiency
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

Error of estimation
The difference between an estimated value and the true value.

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

Event
A subset of a sample space.

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

Gamma function
A function used in the probability density function of a gamma random variable that can be considered to extend factorials

Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

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

Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.