 5.10.1: Consider again the joint distribution of heights of husbands and wi...
 5.10.2: Suppose that two different tests A and B are to be given to a stude...
 5.10.3: Consider again the two tests A and B described in Exercise 2. If a ...
 5.10.4: Consider again the two tests A and B described in Exercise 2. If a ...
 5.10.5: Consider again the two tests A and B described in Exercise 2. If a ...
 5.10.6: Suppose that the random variables X1 and X2 have a bivariate normal...
 5.10.7: Suppose that X1 and X2 have a bivariate normal distribution for whi...
 5.10.8: Let f (x1, x2) denote the p.d.f. of the bivariate normal distributi...
 5.10.9: Let f (x1, x2) denote the p.d.f. of the bivariate normal distributi...
 5.10.10: Suppose that two random variables X1 and X2 have a bivariate normal...
 5.10.11: Suppose that two random variables X1 and X2 have a bivariate normal...
 5.10.12: Suppose that the two measurements from flea beetles in Example 5.10...
 5.10.13: Suppose that the joint p.d.f. of two random variables X and Y is pr...
 5.10.14: Suppose that a random variable X has a normal distribution, and for...
 5.10.15: Let X1,...,Xn be i.i.d. random variables having the normal distribu...
Solutions for Chapter 5.10: Special Distributions
Full solutions for Probability and Statistics  4th Edition
ISBN: 9780321500465
Solutions for Chapter 5.10: Special Distributions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Probability and Statistics was written by and is associated to the ISBN: 9780321500465. This textbook survival guide was created for the textbook: Probability and Statistics, edition: 4. Since 15 problems in chapter 5.10: Special Distributions have been answered, more than 16502 students have viewed full stepbystep solutions from this chapter. Chapter 5.10: Special Distributions includes 15 full stepbystep solutions.

Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

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.

Average
See Arithmetic mean.

Bimodal distribution.
A distribution with two modes

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).

Confounding
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

Contour plot
A twodimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

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 .

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

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.

Deining relation
A subset of effects in a fractional factorial design that deine the aliases in the design.

Demingâ€™s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

Dependent variable
The response variable in regression or a designed experiment.

Designed experiment
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

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

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

Distribution function
Another name for a cumulative distribution function.

Error mean square
The error sum of squares divided by its number of degrees of freedom.

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

Generator
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.