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# Solutions for Chapter 3.2: Reduction of Order

## Full solutions for Advanced Engineering Mathematics | 5th Edition

ISBN: 9781449691721

Solutions for Chapter 3.2: Reduction of Order

Solutions for Chapter 3.2
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##### ISBN: 9781449691721

This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics , edition: 5. Since 23 problems in chapter 3.2: Reduction of Order have been answered, more than 34668 students have viewed full step-by-step solutions from this chapter. Chapter 3.2: Reduction of Order includes 23 full step-by-step solutions. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781449691721.

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).

• 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

• Bivariate distribution

The joint probability distribution of two random variables.

• Block

In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

• Conditional probability

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

• Continuous uniform random variable

A continuous random variable with range of a inite interval and a constant probability density function.

• Contrast

A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

• Correlation

In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

• Covariance

A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

• 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.

• 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

• Curvilinear regression

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

• Deming’s 14 points.

A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

• Design matrix

A matrix that provides the tests that are to be conducted in an experiment.

• 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.

• 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.

• 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.

• Geometric random variable

A discrete random variable that is the number of Bernoulli trials until a success occurs.

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