- 126.96.36.199: Plot the response time distribution (both conditional and unconditi...
- 188.8.131.52: Derive the steady-state probabilities for M/M/m/n queue. Then deriv...
- 184.108.40.206: Plot task completion time distributions for the two-state availabil...
- 220.127.116.11: From the LSTs of the completion time (equations (8.60) and (8.61)),...
- 18.104.22.168: Specify reward assignments to the CTMC of Figure 8.14 for computing...
Solutions for Chapter 8.2.3: Finite State Space
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.
See Arithmetic mean.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
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 method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
Formulas used to determine the number of elements in sample spaces and events.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
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).
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.
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 model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
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 .
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