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# Solutions for Chapter 5.4: CONDITIONAL PROBABILITY AND THE GENERAL MULTIPLICATION RULE

## Full solutions for Statistics: Informed Decisions Using Data | 4th Edition

ISBN: 9780321757272

Solutions for Chapter 5.4: CONDITIONAL PROBABILITY AND THE GENERAL MULTIPLICATION RULE

Solutions for Chapter 5.4
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##### ISBN: 9780321757272

Chapter 5.4: CONDITIONAL PROBABILITY AND THE GENERAL MULTIPLICATION RULE includes 90 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 90 problems in chapter 5.4: CONDITIONAL PROBABILITY AND THE GENERAL MULTIPLICATION RULE have been answered, more than 154869 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Statistics: Informed Decisions Using Data , edition: 4. Statistics: Informed Decisions Using Data was written by and is associated to the ISBN: 9780321757272.

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).

• Bayes’ estimator

An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.

• Bernoulli trials

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

• Binomial random variable

A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

• Block

In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

• 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.

• Chi-square test

Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

• Continuity correction.

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

• 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 coeficient

A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

• 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 .

• 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 .

• Cumulative normal distribution function

The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

• Cumulative sum control chart (CUSUM)

A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

• Defect concentration diagram

A quality tool that graphically shows the location of defects on a part or in a process.

• Discrete distribution

A probability distribution for a discrete random variable

• Enumerative study

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

• Exhaustive

A property of a collection of events that indicates that their union equals the sample space.

• 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

• 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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