- 2.7.1: Let X denote the execution time of a job rounded to the nearest sec...
- 2.7.2: Show that the PGF of a geometric random variable with parameter p i...
- 2.7.3: Let X be a negative binomial random variable with parameters n, p, ...
Solutions for Chapter 2.7: The Probability Generating Function
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
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.
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test
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 distribution with two modes
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
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.
The probability of an event given that the random experiment produces an outcome in another event.
A probability distribution for a continuous random variable.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
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.
An expression sometimes used for nonlinear regression models or polynomial regression models.
The response variable in regression or a designed experiment.
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
A subset of a sample space.
Exponential random variable
A series of tests in which changes are made to the system under study
A signal from a control chart when no assignable causes are present
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.
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
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