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# Solutions for Chapter Chapter 10: Introducing Probability

## Full solutions for The Basic Practice of Statistics | 4th Edition

ISBN: 9780716774785

Solutions for Chapter Chapter 10: Introducing Probability

Solutions for Chapter Chapter 10
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##### ISBN: 9780716774785

The Basic Practice of Statistics was written by and is associated to the ISBN: 9780716774785. This expansive textbook survival guide covers the following chapters and their solutions. Since 56 problems in chapter Chapter 10: Introducing Probability have been answered, more than 7733 students have viewed full step-by-step solutions from this chapter. Chapter Chapter 10: Introducing Probability includes 56 full step-by-step solutions. This textbook survival guide was created for the textbook: The Basic Practice of Statistics, edition: 4.

Key Statistics Terms and definitions covered in this textbook
• 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.

• Bias

An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

• Bivariate normal distribution

The joint distribution of two normal random variables

• Center line

A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

• Conditional mean

The mean of the conditional probability distribution of a random variable.

• Conditional probability density function

The probability density function of the conditional probability distribution of a continuous random variable.

• 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

• Continuous distribution

A probability distribution for a continuous 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.

• Correlation matrix

A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .

• Counting techniques

Formulas used to determine the number of elements in sample spaces and events.

• 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.

• 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.

• 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.

• 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.

• Event

A subset of a sample space.

• F-test

Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

• 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.

• Harmonic mean

The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .

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