- 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 factorial experiment.
A full factorial experiment with k factors and 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.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
Bivariate normal distribution
The joint distribution of two normal random variables
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
Defects-per-unit control chart
See U chart
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.
Another name for a probability density function
Another name for a cumulative distribution function.
The variance of an error term or component in a model.
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
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 .