 6.4.1: Consider a server with Poisson jobarrival stream at an average rat...
 6.4.2: Spareparts problem [BARL 1981]. A system requires k components of ...
 6.4.3: When we considered the decomposition of a Poisson process in the te...
 6.4.4: We are given two independent Poisson arrival streams {Xt  0 t < } ...
 6.4.5: Consider the generalization of the ordinary Poisson process, called...
 6.4.6: Prove Theorem 6.1 starting with Theorem 6.2. (Hint: Refer to the se...
Solutions for Chapter 6.4: The Poisson Process
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications  2nd Edition
ISBN: 9781119285427
Solutions for Chapter 6.4: The Poisson Process
Get Full SolutionsSince 6 problems in chapter 6.4: The Poisson Process have been answered, more than 3403 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Probability and Statistics with Reliability, Queuing, and Computer Science Applications , edition: 2. Probability and Statistics with Reliability, Queuing, and Computer Science Applications was written by and is associated to the ISBN: 9781119285427. Chapter 6.4: The Poisson Process includes 6 full stepbystep solutions.

`error (or `risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

aerror (or arisk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

Acceptance region
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

Addition rule
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).

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.

Assignable cause
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

Bayesâ€™ theorem
An equation for a conditional probability such as PA B (  ) in terms of the reverse conditional probability PB A (  ).

Bivariate normal distribution
The joint distribution of two normal random variables

C chart
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defectsperunit or U chart.

Causal variable
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

Coeficient of determination
See R 2 .

Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.

Correction factor
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 .

Correlation coeficient
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

Dependent variable
The response variable in regression or a designed experiment.

Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

Distribution function
Another name for a cumulative distribution function.

Enumerative study
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.

Fisherâ€™s least signiicant difference (LSD) method
A series of pairwise hypothesis tests of treatment means in an experiment to determine which means differ.