# 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 Patricia and is associated to the ISBN: 9781119285427. Since 5 problems in chapter 4.7: Inequalities And Limit Theorems have been answered, more than 1273 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
• Acceptance region

In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

• 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

• 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.

• Central composite design (CCD)

A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.

• 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.

• Conditional probability density function

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

• 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 region

In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

• Cumulative distribution function

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

• 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

• 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.

• Discrete random variable

A random variable with a inite (or countably ininite) range.

• Dispersion

The amount of variability exhibited by data

• Distribution function

Another name for a cumulative distribution function.

• Enumerative study

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

• Erlang random variable

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

• Factorial experiment

A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

• Generator

Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.

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