- 7.3.1: Consider a system with two components [ASH 1970]. We observe the st...
- 7.3.2: Assume that a computer system is in one of three states: busy, idle...
- 7.3.3: Any transition probability matrix P is a stochastic matrix; that is...
- 7.3.4: Show that the Markov chain of Example 7.12 is irreducible and aperi...
Solutions for Chapter 7.3: State Classification And Limiting Probabilitites
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
A distribution with two modes
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
The variance of the conditional probability distribution of a random variable.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
A matrix that provides the tests that are to be conducted in an experiment.
The amount of variability exhibited by data
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
A study in which a sample from a population is used to make inference to the population. See Analytic study
Error mean square
The error sum of squares divided by its number of degrees of freedom.
Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
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.
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.
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