- 1.1.1: Two towns are connected by a network of communication channels. The...
- 1.1.2: Given three components with respective reliabilities R1 = 0.8, R2 =...
- 1.1.3: Determine the conditions under which an event A is independent of i...
- 1.1.4: General multiplication rule (GMR). Given a list of events A1, A2, ,...
- 1.1.5: Seven lamps are located as shown in Figure 1.P.3. Each lamp can fai...
- 1.1.6: Consider a base repeater in a cellular communication system with tw...
- 1.1.7: Modify the base repeater problem above so that a control can also f...
- 1.1.8: Return to Example 1.13 but now permitting a shared link BC as shown...
Solutions for Chapter 1.1: Independence of Events
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
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
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.
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain
A distribution with two modes
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
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.
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.
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
Formulas used to determine the number of elements in sample spaces and events.
An expression sometimes used for nonlinear regression models or polynomial regression models.
A subset of effects in a fractional factorial design that deine the aliases in the design.
A matrix that provides the tests that are to be conducted in an experiment.
A study in which a sample from a population is used to make inference to the population. See Analytic study
Error of estimation
The difference between an estimated value and the true value.
The variance of an error term or component in a model.
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
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.