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# Solutions for Chapter 1.8: Combinatorial Problems

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

ISBN: 9781119285427

Solutions for Chapter 1.8: Combinatorial Problems

Solutions for Chapter 1.8
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##### ISBN: 9781119285427

This textbook survival guide was created for the textbook: Probability and Statistics with Reliability, Queuing, and Computer Science Applications , edition: 2. Probability and Statistics with Reliability, Queuing, and Computer Science Applications was written by and is associated to the ISBN: 9781119285427. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 1.8: Combinatorial Problems includes 5 full step-by-step solutions. Since 5 problems in chapter 1.8: Combinatorial Problems have been answered, more than 3146 students have viewed full step-by-step solutions from this chapter.

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

In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

• 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

• Alternative hypothesis

In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

• Bias

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

• 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.

• Cause-and-effect diagram

A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

• 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.

• Conditional probability mass function

The probability mass function of the conditional probability distribution of a discrete 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.

• Counting techniques

Formulas used to determine the number of elements in sample spaces and events.

• 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.

• Discrete uniform random variable

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

• Error mean square

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

• Error of estimation

The difference between an estimated value and the true value.

• Error propagation

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

• F distribution.

The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.

• Gamma function

A function used in the probability density function of a gamma random variable that can be considered to extend factorials

• 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 .

• 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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