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# Solutions for Chapter 12.4: Inferences Concerning mY ? x* and the Prediction of Future Y Values ## Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition

ISBN: 9781305251809 Solutions for Chapter 12.4: Inferences Concerning mY ? x* and the Prediction of Future Y Values

Solutions for Chapter 12.4
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##### ISBN: 9781305251809

This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences, edition: 9. Since 13 problems in chapter 12.4: Inferences Concerning mY ? x* and the Prediction of Future Y Values have been answered, more than 79595 students have viewed full step-by-step solutions from this chapter. Probability and Statistics for Engineering and the Sciences was written by and is associated to the ISBN: 9781305251809. Chapter 12.4: Inferences Concerning mY ? x* and the Prediction of Future Y Values includes 13 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their 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).

• Analysis of variance (ANOVA)

A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

• Asymptotic relative eficiency (ARE)

Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.

• 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.

• 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.

• Bayes’ theorem

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

• Bias

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

• Chi-square (or chi-squared) random variable

A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma 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.

• Decision interval

A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.

• Degrees of freedom.

The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

• Density function

Another name for a probability density function

• Discrete uniform random variable

A discrete random variable with a inite range and constant probability mass function.

• 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.

• Erlang random variable

A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

• Error of estimation

The difference between an estimated value and the true value.

• Fraction defective

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

• Fraction defective control chart

See P chart

• Gamma random variable

A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

• 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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