- 10.2.2 .1: Show that the maximum-likelihood estimator of the mean life with a ...
- 10.2.2 .2: Suppose that the CPU service time X of a job is gamma-distributed w...
- 10.2.2 .3: Derive the MLE estimates of the parameters a, , and of the log-logi...
- 10.2.2 .4: Show that the MLE estimates of the parameters of the Pareto distrib...
Solutions for Chapter 10.2.2 : Maximum-Likelihood Estimation
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
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
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).
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.
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.
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.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
A probability distribution for a continuous random variable.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
Formulas used to determine the number of elements in sample spaces and events.
A subset of effects in a fractional factorial design that deine the aliases in the design.
Discrete random variable
A random variable with a inite (or countably ininite) range.
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
The amount of variability exhibited by data
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
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.
Estimate (or point estimate)
The numerical value of a point estimator.
Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function