- Chapter 1.1: Independence of Events
- Chapter 1.12: Bernoulli Trials
- Chapter 1.3: Sample Space
- Chapter 1.5: Algebra Of Events
- Chapter 1.8: Combinatorial Problems
- Chapter 1.9: Conditional Probability
- Chapter 10.2: Parameter Estimation
- Chapter 10.2.2 : Maximum-Likelihood Estimation
- Chapter 10.2.3.1 : Sampling from the Normal Distribution.
- Chapter 10.2.3.2: Sampling from the Exponential Distribution.
- Chapter 10.2.3.4: Sampling from the Bernoulli Distribution.
- Chapter 10.2.4.4: Estimation for a Semi-Markov Process.
- Chapter 10.2.5: Estimation with Dependent Samples
- Chapter 10.3.1: Tests on the Population Mean
- Chapter 10.3.2: Hypotheses Concerning Two Means
- Chapter 11.2: Least-Squares Curve Fitting
- Chapter 11.3: The Coefficients of Determination
- Chapter 11.4: Confidence Intervals In Linear Regression
- Chapter 11.6: Correlation Analysis
- Chapter 11.7: Simple Nonlinear Regression
- Chapter 11.8: HIGHER-DIMENSIONAL LEAST-SQUARES FIT
- Chapter 11.9: Analysiis And Variance
- Chapter 2: Random Variables and Their Event Spaces
- Chapter 2.5.8 : Constant Random Variable
- Chapter 2.6: Analysis of Program Mix
- Chapter 2.7: The Probability Generating Function
- Chapter 2.9: Independent Random Vaariables
- Chapter 3.2: The Exponential Contribution
- Chapter 126.96.36.199: The Exponential Contribution
- Chapter 3.4: Some Important Distributions
- Chapter 3.4.9: Defective Contribution
- Chapter 3.5: Functions of a Random Variables
- Chapter 3.6: Jointly Distributed Random Variables
- Chapter 3.7: Order Statistics
- Chapter 3.8: Distribution Of Sums
- Chapter 3.9: Functions Of Normal Random Variables
- Chapter 4: Moments
- Chapter 4.3: Expectation Based On Multiple Random Variables
- Chapter 4.5.14: The Normal Distribution
- Chapter 4.6: Computation Of Mean Time To Failure
- Chapter 4.7: Inequalities And Limit Theorems
- Chapter 5.1: Introduction
- Chapter 5.2: Mixture And Distributions
- Chapter 5.3: Conditional Expectation
- Chapter 5.4: Imperfect Fault Coverage And Reliability
- Chapter 5.5: Random Sums
- Chapter 6.1: Introduction
- Chapter 6.2: Clasification Of Stochastic Processes
- Chapter 6.3: The Bernoulli Process
- Chapter 6.4: The Poisson Process
- Chapter 6.6: Availability Analysis
- Chapter 6.7: Random Incidence
- Chapter 7.2: Computation Of n-Step Transition Probabilities
- Chapter 7.3: State Classification And Limiting Probabilitites
- Chapter 7.5: Markov Modulated Bernoulli Process
- Chapter 7.6: Irreducible Finite Chains With Aperiodic States
- Chapter 188.8.131.52 : The LRU Stack Model [SPIR 1977].
- Chapter 7.6.3: Slotted Aloha Model
- Chapter 7.7: The M/G/ 1 Queuing System
- Chapter 7.9: Finite Markov Chains With Absorbing States
- Chapter 8.1: Introduction
- Chapter 8.2: The Birth-Death Process
- Chapter 8.2.3: Finite State Space
- Chapter 184.108.40.206: Machine Repairman Mdoel
- Chapter 220.127.116.11 : Wireless Handoff Performance Model.
- Chapter 8.3.1: The Pure Birth Process
- Chapter 18.104.22.168: Death Process with a Linear Rate.
- Chapter 8.4.1: Availability Models
- Chapter 22.214.171.124 : The MMPP/M/1 Queue.
- Chapter 8.5: Markov Chains With Absorbing States
- Chapter 126.96.36.199: Successive Overrelaxation (SOR).
- Chapter 188.8.131.52 : Numerical Methods.
- Chapter 8.7.2 : Stochastic Petri Nets
- Chapter 8.7.4 : Stochastic Reward Nets
- Chapter 9.1: Intoduction
- Chapter 9.2: Open Queing Networks
- Chapter 9.3: Closed Queuing Networks
- Chapter 9.4: General Service Distribution And Mulitiple Job Types
- Chapter 9.5: Non-Product-Form Networks
- Chapter 9.6.2 : Response Time Distribution in Closed Networks
- Chapter 9.7: Summary
Probability and Statistics with Reliability, Queuing, and Computer Science Applications 2nd Edition - Solutions by Chapter
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition - Solutions by ChapterGet Full Solutions
Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
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.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
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.
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
The variance of the conditional probability distribution of a random variable.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.
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.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Discrete random variable
A random variable with a inite (or countably ininite) range.
Estimate (or point estimate)
The numerical value of a point estimator.
A subset of a sample space.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.