- 4.7.1: The average CPU time per request is known to be 4.39 s for a comput...
- 4.7.2: Using the normal tables, plot P(|X| ) for 0 << 3, where X N(0, 1). ...
- 4.7.3: Consider a random variable X with the Cauchy pdf:f(x) = 1(1 + x2), ...
- 4.7.4: Construct an example of a discrete random variable X that takes on ...
- 4.7.5: In order to represent a nonnegative real number X in a computer wit...
Solutions for Chapter 4.7: Inequalities And Limit Theorems
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
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
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
The mean of the conditional probability distribution of a random variable.
The probability of an event given that the random experiment produces an outcome in another event.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Another name for a probability density function
Discrete random variable
A random variable with a inite (or countably ininite) range.
Estimate (or point estimate)
The numerical value of a point estimator.
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.
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.
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 .
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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