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# Solutions for Chapter 1.6: Introduction to Probability

## Full solutions for Probability and Statistics | 4th Edition

ISBN: 9780321500465

Solutions for Chapter 1.6: Introduction to Probability

Solutions for Chapter 1.6
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##### ISBN: 9780321500465

This expansive textbook survival guide covers the following chapters and their solutions. Since 8 problems in chapter 1.6: Introduction to Probability have been answered, more than 15110 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Probability and Statistics, edition: 4. Probability and Statistics was written by and is associated to the ISBN: 9780321500465. Chapter 1.6: Introduction to Probability includes 8 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook

A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

• 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.

A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Backward elimination

A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain

• C chart

An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.

• 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 mean

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

• Contingency table.

A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

• Continuity correction.

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

• Continuous distribution

A probability distribution for a continuous random variable.

• Contrast

A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

• 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.

• Correlation

In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

• 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 .

• 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.

• False alarm

A signal from a control chart when no assignable causes are present

• 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

• Fraction defective

In statistical quality control, that portion of a number of units or the output of a process that is defective.

• 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

• Geometric mean.

The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .

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