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# Solutions for Chapter 4.7: Inequalities And Limit Theorems

## Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition

ISBN: 9781119285427

Solutions for Chapter 4.7: Inequalities And Limit Theorems

Solutions for Chapter 4.7
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##### ISBN: 9781119285427

This expansive textbook survival guide covers the following chapters and their solutions. Chapter 4.7: Inequalities And Limit Theorems includes 5 full step-by-step solutions. Probability and Statistics with Reliability, Queuing, and Computer Science Applications was written by and is associated to the ISBN: 9781119285427. Since 5 problems in chapter 4.7: Inequalities And Limit Theorems have been answered, more than 2654 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Probability and Statistics with Reliability, Queuing, and Computer Science Applications , edition: 2.

Key Statistics Terms and definitions covered in this textbook
• `-error (or `-risk)

In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

• 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

• Axioms of probability

A set of rules that probabilities deined on a sample space must follow. See Probability

• Bias

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

• Bivariate distribution

The joint probability distribution of two random variables.

• 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.

• 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.

• Central tendency

The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

• 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.

• Control limits

See Control chart.

• Correction factor

A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

• Curvilinear regression

An expression sometimes used for nonlinear regression models or polynomial regression models.

• Deming

W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

• Distribution function

Another name for a cumulative distribution function.

• Error mean square

The error sum of squares divided by its number of degrees of freedom.

• Error variance

The variance of an error term or component in a model.

• Fixed factor (or fixed effect).

In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

• Forward selection

A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

• Hat matrix.

In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .

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