# Solutions for Chapter 10: Discrete Data Analysis

## Full solutions for Probability and Statistics for Engineers and Scientists | 4th Edition

ISBN: 9781111827045

Solutions for Chapter 10: Discrete Data Analysis

Solutions for Chapter 10
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##### ISBN: 9781111827045

This expansive textbook survival guide covers the following chapters and their solutions. Since 94 problems in chapter 10: Discrete Data Analysis have been answered, more than 5848 students have viewed full step-by-step solutions from this chapter. Probability and Statistics for Engineers and Scientists was written by Patricia and is associated to the ISBN: 9781111827045. Chapter 10: Discrete Data Analysis includes 94 full step-by-step solutions. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and Scientists, edition: 4.

Key Statistics Terms and definitions covered in this textbook
• 2 k factorial experiment.

A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Bivariate normal distribution

The joint distribution of two normal random variables

• Cause-and-effect diagram

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

• 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

The probability of an event given that the random experiment produces an outcome in another event.

• Conidence level

Another term for the conidence coeficient.

• Continuous distribution

A probability distribution for a continuous random variable.

• Contour plot

A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

• Convolution

A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

• 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 .

• 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).

• 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.

• Deming

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

• Discrete distribution

A probability distribution for a discrete random variable

• Empirical model

A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

• 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.

• Fisher’s least signiicant difference (LSD) method

A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.

• Harmonic mean

The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .

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