- 10.2.4.4.1: For an M/M/1 queue, 955 arrivals were observed in a period of 1000 ...
- 10.2.4.4.2: Give an argument for determining a 100(1 )% confidence interval for...
- 10.2.4.4.3: We have noted (in Chapter 8) that in an M/M/1 queue the response ti...
Solutions for Chapter 10.2.4.4: Estimation for a Semi-Markov Process.
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
See Arithmetic mean.
Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data
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.
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.
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.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
See Control chart.
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 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 .
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
A matrix that provides the tests that are to be conducted in an experiment.
A series of tests in which changes are made to the system under study
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
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.
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
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.
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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