- 8.2.1: Consider an M/M/1 queue with an arrival rate and the service rate ....
- 8.2.2: A group of telephone subscribers is observed continuously during a ...
- 8.2.3: Consider an M/M/1 queuing system in which the total number of jobs ...
- 8.2.4: The arrival of large jobs at a server forms a Poisson process with ...
- 8.2.5: Let the random variable Tk denote the holding time in state k of th...
- 8.2.6: Derive an expression for the frequency of entering state 0 (server ...
- 8.2.7: Define the perceived mean queue length [GEIS 1983] N = E[N2]/E[N] a...
Solutions for Chapter 8.2: The Birth-Death Process
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
A distribution with two modes
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
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.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
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 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 .
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
An expression sometimes used for nonlinear regression models or polynomial regression models.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
The response variable in regression or a designed experiment.
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.
Error of estimation
The difference between an estimated value and the true value.
Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.
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.
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r
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