- 8.1.1: Show that the solution to the matrix equation (8.17) with the initi...
- 8.1.2: Show that the solution to the matrixvector equation (8.18) can be w...
- 8.1.3: Show that the solution to the matrixvector equation (8.19) can be w...
- 8.1.4: Show that the solution to equation (8.14) for a nonhomogeneous CTMC...
- 8.1.5: For a homogeneous CTMC show that the Laplace transform of the trans...
- 8.1.6: Show that the integral (convolution) form of the Kolmogorov forward...
- 8.1.7: Show that 0 = 0 is an eigenvalue of the generator matrix Q.
Solutions for Chapter 8.1: Introduction
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).
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
Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
A distribution with two modes
The joint probability distribution of two random variables.
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
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
Another term for the conidence coeficient.
A probability distribution for a continuous random variable.
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).
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
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).
Error mean square
The error sum of squares divided by its number of degrees of freedom.
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.
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
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .
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