- 7.3.1: Customers arrive at a postoffice at a Poisson rate of three per min...
- 7.3.2: Find the median of an exponential random variable with rate . Recal...
- 7.3.3: Let X be an exponential random variable with mean 1. Find the proba...
- 7.3.4: The time between the first and second heart attacks for a certain g...
- 7.3.5: Guests arrive at a hotel, in accordance with a Poisson process, at ...
- 7.3.6: Let X be an exponential random variable with parameter . Find P !D ...
- 7.3.7: Suppose that, at an Italian restaurant, the time, in minutes, betwe...
- 7.3.8: Suppose that the time it takes for a novice secretary to type a doc...
- 7.3.9: The profit is $350 for each computer assembled by a certain person....
- 7.3.10: Mr. Jones is waiting to make a phone call at a train station. There...
- 7.3.11: In a factory, a certain machine operates for a period which is expo...
- 7.3.12: In data communication, messages are usually combinations of charact...
- 7.3.13: The random variable X is called double exponentially distributed if...
- 7.3.14: Let X, the lifetime (in years) of a radio tube, be exponentially di...
- 7.3.15: Prove that if X is a positive, continuous, memoryless random variab...
Solutions for Chapter 7.3: Exponential Random Variables
Full solutions for Fundamentals of Probability, with Stochastic Processes | 3rd Edition
`-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).
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
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
See Arithmetic mean.
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.
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
The mean of the conditional probability distribution of a random variable.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.
Another name for a probability density function
The response variable in regression or a designed experiment.
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.
Exponential random variable
A series of tests in which changes are made to the system under study
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
A signal from a control chart when no assignable causes are present
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
In statistical quality control, that portion of a number of units or the output of a process that is defective.