- 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
The joint probability distribution of two random variables.
Bivariate normal distribution
The joint distribution of two normal random variables
Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
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.
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
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
The variance of the conditional probability distribution of a random variable.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
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
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
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
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.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
Fraction defective control chart
See P chart
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function