Solutions for Chapter 9: Decision Theory
Full solutions for Mathematical Statistics with Applications  8th Edition
ISBN: 9780321807090
Solutions for Chapter 9: Decision Theory
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Assignable cause
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

Bivariate normal distribution
The joint distribution of two normal random variables

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.

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

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

Control limits
See Control chart.

Convolution
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

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

Designed experiment
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

Dispersion
The amount of variability exhibited by data

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.

Expected value
The expected value of a random variable X is its longterm average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

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

Forward selection
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

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

Gaussian distribution
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

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.