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# Solutions for Chapter 2.2: Density Curves and Normal Distributions

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

ISBN: 9781464108730

Solutions for Chapter 2.2: Density Curves and Normal Distributions

Solutions for Chapter 2.2
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##### ISBN: 9781464108730

The Practice of Statistics was written by and is associated to the ISBN: 9781464108730. Since 44 problems in chapter 2.2: Density Curves and Normal Distributions have been answered, more than 24567 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. Chapter 2.2: Density Curves and Normal Distributions includes 44 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Key Statistics Terms and definitions covered in this textbook
• 2 k factorial experiment.

A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

• 2 k p - factorial experiment

A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

• Attribute control chart

Any control chart for a discrete random variable. See Variables control chart.

• Average

See Arithmetic mean.

• 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

• Biased estimator

Unbiased estimator.

• Bivariate distribution

The joint probability distribution of two random variables.

• Box plot (or box and whisker plot)

A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

• 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.

• Continuity correction.

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

• 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.

• Cook’s distance

In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

• 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.

• Error propagation

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

• Error sum of squares

In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.

• Estimate (or point estimate)

The numerical value of a point estimator.

• 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.

• Gamma function

A function used in the probability density function of a gamma random variable that can be considered to extend factorials

• Generating function

A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function

• Hat matrix.

In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .

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