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# Solutions for Chapter 5.3: Independence and the Multiplication Rule

## Full solutions for Statistics: Informed Decisions Using Data | 5th Edition

ISBN: 9780134133539

Solutions for Chapter 5.3: Independence and the Multiplication Rule

Solutions for Chapter 5.3
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##### ISBN: 9780134133539

Summary of Chapter 5.3: Independence and the Multiplication Rule

Identify independent events. Use the Multiplication Rule for Independent Events. Compute at-least probabilities

This textbook survival guide was created for the textbook: Statistics: Informed Decisions Using Data, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions. Statistics: Informed Decisions Using Data was written by and is associated to the ISBN: 9780134133539. Chapter 5.3: Independence and the Multiplication Rule includes 34 full step-by-step solutions. Since 34 problems in chapter 5.3: Independence and the Multiplication Rule have been answered, more than 27069 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
• 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

• 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

• Average

See Arithmetic mean.

• Bayes’ theorem

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

• Causal variable

When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

• Completely randomized design (or experiment)

A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

• Conditional probability density function

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

• Correlation coeficient

A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

• 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.

• 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.

• Defects-per-unit control chart

See U chart

• Design matrix

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

• Discrete uniform random variable

A discrete random variable with a inite range and constant probability mass function.

• Distribution free method(s)

Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

• Error of estimation

The difference between an estimated value and the true value.

• Error variance

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

• Gamma random variable

A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

• 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

• Harmonic mean

The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .