- 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
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.
See Arithmetic mean.
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).
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.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
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.
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.
A subset of effects in a fractional factorial design that deine the aliases in the design.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
The response variable in regression or a 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.
Another name for a cumulative distribution function.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
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
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.