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# Solutions for Chapter 5: Understanding and Comparing Distributions ## Full solutions for Stats: Modeling The World | 3rd Edition

ISBN: 9780131359581 Solutions for Chapter 5: Understanding and Comparing Distributions

Solutions for Chapter 5
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##### ISBN: 9780131359581

This expansive textbook survival guide covers the following chapters and their solutions. Stats: Modeling The World was written by and is associated to the ISBN: 9780131359581. Since 42 problems in chapter 5: Understanding and Comparing Distributions have been answered, more than 44574 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Stats: Modeling The World , edition: 3. Chapter 5: Understanding and Comparing Distributions includes 42 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook
• Acceptance region

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

• Attribute control chart

Any control chart for a discrete random variable. See Variables control chart.

• Average

See Arithmetic mean.

• Bayes’ theorem

An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).

• Central limit theorem

The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

• Conditional probability mass function

The probability mass function of the conditional probability distribution of a discrete random variable.

• 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.

• Defect

Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

• Discrete random variable

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

• Empirical model

A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

• Error variance

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

• Estimate (or point estimate)

The numerical value of a point estimator.

• Experiment

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

• Exponential random variable

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

• First-order model

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

• Fractional factorial experiment

A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

• Gamma function

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

• Generating function

A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function

• 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.

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