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# Solutions for Chapter 6.1: Discrete and Continuous Random Variables

## Full solutions for The Practice of Statistics | 5th Edition

ISBN: 9781464108730

Solutions for Chapter 6.1: Discrete and Continuous Random Variables

Solutions for Chapter 6.1
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##### ISBN: 9781464108730

Since 34 problems in chapter 6.1: Discrete and Continuous Random Variables have been answered, more than 6102 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: The Practice of Statistics, edition: 5. The Practice of Statistics was written by and is associated to the ISBN: 9781464108730. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 6.1: Discrete and Continuous Random Variables includes 34 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook
• Bias

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

• Bimodal distribution.

A distribution with two modes

• 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.

• Continuity correction.

A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

• 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

In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

• 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.

• Dependent variable

The response variable in regression or a designed experiment.

• 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.

• Exponential random variable

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

• False alarm

A signal from a control chart when no assignable causes are present

• 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.

• 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.

• 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

• Geometric random variable

A discrete random variable that is the number of Bernoulli trials until a success occurs.

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