- 22.214.171.124 .1: Consider an M/M/ queuing system (refer to problem 4 in Section 8.2....
- 126.96.36.199 .2: Consider an M/M/1/2 queuing system and find the transient state pro...
- 188.8.131.52 .3: Find the transient state probabilities for Example 8.19 using the L...
- 184.108.40.206 .4: Compute the transient solution for Example 8.35 numerically using r...
Solutions for Chapter 220.127.116.11 : Numerical Methods.
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
Formulas used to determine the number of elements in sample spaces and events.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
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.
Another name for a probability density function
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
Discrete random variable
A random variable with a inite (or countably ininite) range.
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.
Estimate (or point estimate)
The numerical value of a point estimator.
A signal from a control chart when no assignable causes are present
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.
Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.