- 188.8.131.52.1: Show that the matrix Q defined by equation (8.133) is a DTMC matrix.
- 184.108.40.206.2: Show that with condition (8.135), Q is an aperiodic matrix.
- 220.127.116.11.3: Perform steady-state analysis of the CTMC model in Example 8.23 (Fi...
- 18.104.22.168.4: Apply the power method to the CTMC of Figure 8.P.4 to obtain an exp...
- 22.214.171.124.5: Suppose that we are interested in computing the derivative d/d with...
- 126.96.36.199.6: Show that the GaussSeidel iteration matrix for the CTMC of Figure 8...
Solutions for Chapter 188.8.131.52: Successive Overrelaxation (SOR).
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
See Arithmetic mean.
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
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.
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.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
A probability distribution for a continuous random variable.
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.
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.
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
Defects-per-unit control chart
See U chart
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Exponential random variable
A series of tests in which changes are made to the system under study
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
Fraction defective control chart
See P chart
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
A function used in the probability density function of a gamma random variable that can be considered to extend factorials