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Get Full Access to Statistics - Textbook Survival Guide
Get Full Access to Statistics - Textbook Survival Guide
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# Solutions for Chapter 5: Continuous Random Variables

## Full solutions for Introduction to Probability | 1st Edition

ISBN: 9781466575578

Solutions for Chapter 5: Continuous Random Variables

Solutions for Chapter 5
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##### ISBN: 9781466575578

This expansive textbook survival guide covers the following chapters and their solutions. Introduction to Probability was written by and is associated to the ISBN: 9781466575578. Chapter 5: Continuous Random Variables includes 61 full step-by-step solutions. This textbook survival guide was created for the textbook: Introduction to Probability, edition: 1. Since 61 problems in chapter 5: Continuous Random Variables have been answered, more than 9992 students have viewed full step-by-step solutions from this chapter.

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.

• Alternative hypothesis

In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

• Bayes’ estimator

An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.

• Biased estimator

Unbiased estimator.

• Bivariate normal distribution

The joint distribution of two normal 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.

• 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 mean

The mean of the conditional probability distribution of a random variable.

• Conditional probability density function

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

• Control limits

See Control chart.

• 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.

• 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.

• Defects-per-unit control chart

See U chart

• Eficiency

A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

• Estimate (or point estimate)

The numerical value of a point estimator.

• 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.

• 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

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