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Solutions for Chapter 10.1: Expected Values of Sums of Random Variables

Full solutions for Fundamentals of Probability, with Stochastic Processes | 3rd Edition

ISBN: 9780131453401

Solutions for Chapter 10.1: Expected Values of Sums of Random Variables

Solutions for Chapter 10.1
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ISBN: 9780131453401

This textbook survival guide was created for the textbook: Fundamentals of Probability, with Stochastic Processes, edition: 3. Chapter 10.1: Expected Values of Sums of Random Variables includes 20 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Fundamentals of Probability, with Stochastic Processes was written by and is associated to the ISBN: 9780131453401. Since 20 problems in chapter 10.1: Expected Values of Sums of Random Variables have been answered, more than 15350 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook

A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

• Additivity property of x 2

If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.

• Asymptotic relative eficiency (ARE)

Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.

• 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

• Bias

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

• Bivariate normal distribution

The joint distribution of two normal random variables

• Chance cause

The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

• Conditional probability density function

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

• Conditional variance.

The variance of the conditional probability distribution of a 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.

• 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.

• 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 matrix

A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .

• Curvilinear regression

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

• 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.

• Defect

Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

• 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.

• Estimator (or point estimator)

A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

• 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.

• First-order model

A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model

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