Solutions for Chapter 6: Special Probability Densities
Full solutions for Mathematical Statistics with Applications  8th Edition
ISBN: 9780321807090
Solutions for Chapter 6: Special Probability Densities
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2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

Block
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

Chisquare (or chisquared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

Coeficient of determination
See R 2 .

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

Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

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

Covariance
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 .

Critical value(s)
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

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

Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

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

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

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

Deming
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

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.

Estimate (or point estimate)
The numerical value of a point estimator.

Exponential random variable
A series of tests in which changes are made to the system under study

Firstorder model
A model that contains only irstorder terms. For example, the irstorder response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irstorder model is also called a main effects model

Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.