- 1.8.1: Give the proof of the relation (Re) in this section.
- 1.8.2: Consider a pool of six I/O (input/output) buffers. Assume that any ...
- 1.8.3: Show that if event B is contained in event A, then P(B) P(A).
- 1.8.5: In a party of five persons, compute the probability that at least t...
- 1.8.6: A series of n jobs arrive at a multiprocessor computer with n proce...
Solutions for Chapter 1.8: Combinatorial Problems
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).
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.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
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.
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.
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
A matrix that provides the tests that are to be conducted in an experiment.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
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 signal from a control chart when no assignable causes are present
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
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