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Solutions for Chapter 4.8: Discrete Random Variables and Their Probability Distributions 158 Random Variables

Full solutions for Introduction to Probability and Statistics 1 | 14th Edition

ISBN: 9781133103752

Solutions for Chapter 4.8: Discrete Random Variables and Their Probability Distributions 158 Random Variables

Solutions for Chapter 4.8
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ISBN: 9781133103752

Since 58 problems in chapter 4.8: Discrete Random Variables and Their Probability Distributions 158 Random Variables have been answered, more than 10337 students have viewed full step-by-step solutions from this chapter. Chapter 4.8: Discrete Random Variables and Their Probability Distributions 158 Random Variables includes 58 full step-by-step solutions. Introduction to Probability and Statistics 1 was written by and is associated to the ISBN: 9781133103752. This textbook survival guide was created for the textbook: Introduction to Probability and Statistics 1, edition: 14. This expansive textbook survival guide covers the following chapters and their solutions.

Key Statistics Terms and definitions covered in this textbook
• Analysis of variance (ANOVA)

A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

• Attribute

A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

• Bias

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

• Bivariate distribution

The joint probability distribution of two random variables.

• Bivariate normal distribution

The joint distribution of two normal random variables

• Combination.

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

• Components of variance

The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

• Conditional variance.

The variance of the conditional probability distribution of a 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

• Continuous random variable.

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

• 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.

• 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.

• 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.

• Error variance

The variance of an error term or component in a model.

• Expected value

The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

• Experiment

A series of tests in which changes are made to the system under study

• F-test

Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

• 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

• Fixed factor (or fixed effect).

In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

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