- 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
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each
Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
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).
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous 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 correction factor used to improve the approximation to binomial probabilities from a normal distribution.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
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.
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 square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
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.
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .
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