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# Solutions for Chapter 14: From Randomness to Probability

## Full solutions for Stats: Modeling The World | 3rd Edition

ISBN: 9780131359581

Solutions for Chapter 14: From Randomness to Probability

Solutions for Chapter 14
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##### ISBN: 9780131359581

This textbook survival guide was created for the textbook: Stats: Modeling The World , edition: 3. Since 44 problems in chapter 14: From Randomness to Probability have been answered, more than 38839 students have viewed full step-by-step solutions from this chapter. Chapter 14: From Randomness to Probability includes 44 full step-by-step solutions. 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.

Key Statistics Terms and definitions covered in this textbook
• Additivity property of x 2

If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.

• Alias

In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Analytic study

A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

• Chance cause

The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

• 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

• Consistent estimator

An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

• Contour plot

A two-dimensional 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 in-control 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 in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

• 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.

• Covariance matrix

A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

• 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.

• Dependent variable

The response variable in regression or a designed experiment.

• Dispersion

The amount of variability exhibited by data

• Distribution free method(s)

Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

• Enumerative study

A study in which a sample from a population is used to make inference to the population. See Analytic study

• F distribution.

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

• 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

• 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.

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