- 6.2.1: Show that the time that a discrete-time homogeneous Markov chain sp...
- 6.2.2: Assuming that the number of arrivals in the interval (0, t] is Pois...
- 6.2.3: Consider a stochastic process defined on a finite sample space with...
- 6.2.4: Show that the autocorrelation function R(t1, t2) of a strict-sense ...
Solutions for Chapter 6.2: Clasification Of Stochastic Processes
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
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.
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
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.
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
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.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
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 square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
A subset of a sample space.
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
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .
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