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# Solutions for Chapter 1.4: Basic Theorems ## Full solutions for Fundamentals of Probability, with Stochastic Processes | 3rd Edition

ISBN: 9780131453401 Solutions for Chapter 1.4: Basic Theorems

Solutions for Chapter 1.4
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##### ISBN: 9780131453401

Since 32 problems in chapter 1.4: Basic Theorems have been answered, more than 15010 students have viewed full step-by-step solutions from this chapter. 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. Chapter 1.4: Basic Theorems includes 32 full step-by-step solutions. This textbook survival guide was created for the textbook: Fundamentals of Probability, with Stochastic Processes, edition: 3.

Key Statistics Terms and definitions covered in this textbook
• Acceptance region

In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

• 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

• 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

• Bayes’ theorem

An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).

• Bias

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

• Categorical data

Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

• Cause-and-effect diagram

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

• Combination.

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

• Control limits

See Control chart.

• 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 .

• 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.

• Crossed factors

Another name for factors that are arranged in a factorial experiment.

• Cumulative distribution function

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

• Density function

Another name for a probability density function

• Discrete random variable

A random variable with a inite (or countably ininite) range.

• Error of estimation

The difference between an estimated value and the true value.

• F distribution.

The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.

• Fraction defective

In statistical quality control, that portion of a number of units or the output of a process that is defective.

• Fraction defective control chart

See P chart

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