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# Solutions for Chapter 11: Hypothesis Testing

## Full solutions for Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers | 3rd Edition

ISBN: 9781118324561

Solutions for Chapter 11: Hypothesis Testing

Solutions for Chapter 11
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##### ISBN: 9781118324561

Chapter 11: Hypothesis Testing includes 45 full step-by-step solutions. This textbook survival guide was created for the textbook: Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers, edition: 3. Since 45 problems in chapter 11: Hypothesis Testing have been answered, more than 11077 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers was written by and is associated to the ISBN: 9781118324561.

Key Statistics Terms and definitions covered in this textbook
• Alias

In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• All possible (subsets) regressions

A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

• 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

• Bivariate distribution

The joint probability distribution of two random variables.

• 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.

• Chi-square test

Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

• Combination.

A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

• Conditional probability distribution

The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

• Conidence level

Another term for the conidence coeficient.

• Continuous random variable.

A random variable with an interval (either inite or ininite) of real numbers for its range.

• 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.

• 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.

• 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.

• Erlang random variable

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

• Event

A subset of a sample space.

• Exhaustive

A property of a collection of events that indicates that their union equals the sample space.

• Gaussian distribution

Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

• 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 .

• 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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