- 9.1.1: In Chapter 8 we derived the distribution function of the response t...
- 9.1.2: Consider an M/G/1 queue with FCFS scheduling . Let the random varia...
- 9.1.3: Using the result of problem 2, show that in the M/G/1 case, the squ...
- 9.1.4: Show that the interdeparture time distribution of an M/M/m FCFS que...
Solutions for Chapter 9.1: Intoduction
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion
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
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
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
See Arithmetic mean.
The joint probability distribution of two random variables.
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.
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.
Another term for the conidence coeficient.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Another name for a probability density function
Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
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.
Exponential random variable
A series of tests in which changes are made to the system under study
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
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