- 2.5.8 .1: Show that the limit as k of Pc(k) is zero in equation (2.6).
- 2.5.8 .2: Out of a job population of ten jobs with six jobs of class 1 and fo...
- 2.5.8 .3: A mischievous student wants to break into a computer file, which is...
- 2.5.8 .4: A telephone call may pass through a series of trunks before reachin...
- 2.5.8 .5: Assume that the probability of error-free transmission of a message...
- 2.5.8 .6: One percent of faults occurring in a highly available system need t...
- 2.5.8 .7: Five percent of the disk controllers produced by a plant are known ...
- 2.5.8 .8: The probability of error in the transmission of a bit over a commun...
- 2.5.8 .9: Assume that the number of messages input to a communication channel...
- 2.5.8 .10: VLSI chips, essential to the running of a computer system, fail in ...
Solutions for Chapter 2.5.8 : Constant Random Variable
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
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).
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
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.
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
A matrix that provides the tests that are to be conducted in an experiment.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
A signal from a control chart when no assignable causes are present
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
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.
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.
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
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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