- 126.96.36.199: Consider an database server designed to handle a maximum of 15 tran...
- 188.8.131.52: The CPU time requirement X of a typical job can be modeled by the f...
- 184.108.40.206: The CPU time requirement, T, for jobs has a gamma distribution with...
- 220.127.116.11: A telephone exchange can handle at most 20 simultaneous conversatio...
- 18.104.22.168: For the three parameter Weibull distribution [formula (3.33)], find...
- 22.214.171.124: The time to failure distribution of Tandem software was found to be...
Solutions for Chapter 4.5.14: The Normal Distribution
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.
The mean of the conditional probability distribution of a random variable.
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 measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .
Another name for factors that are arranged in a factorial experiment.
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.
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
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
A study in which a sample from a population is used to make inference to the population. See Analytic study
A series of tests in which changes are made to the system under study
In statistical quality control, that portion of a number of units or the output of a process that is defective.
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.