- 12.2.1: Eq. (12.2.4) is based on the assumption that Z has approximately a ...
- 12.2.2: . In Example 12.2.11, how large would v need to be according to Eq....
- 12.2.3: Suppose that we have available as many i.i.d. standard normal rando...
- 12.2.4: Use a pseudo-random number generator to simulate a sample of 15 ind...
- 12.2.5: Use a pseudo-random number generator to simulate a sample of 15 ind...
- 12.2.6: Suppose that X and Y are independent, that X has the beta distribut...
- 12.2.7: Consider the numbers in Table 10.40 on page 676. Suppose that you h...
- 12.2.8: Consider the same situation described in Exercise 7. This time, con...
- 12.2.9: In Example 12.2.12, we can actually compute the median of the distr...
- 12.2.10: Let X1,...,X21 be i.i.d. with the exponential distribution that has...
- 12.2.11: In Example 12.2.4, there is a slightly simpler way to simulate a sa...
- 12.2.12: Let (Y1, W1), . . . , (Yn, Wn) be an i.i.d. sample of random vector...
- 12.2.13: Use the two-dimensional delta method from Exercise 12 to derive the...
- 12.2.14: Let Y be a random variable with some distribution. Suppose that you...
- 12.2.15: Let Y be a random variable with some distribution. Suppose that you...
- 12.2.16: Consider a queue to which customers arrive according to a Poisson p...
Solutions for Chapter 12.2: Simulation
Full solutions for Probability and Statistics | 4th 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
Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
Another term for the conidence coeficient.
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.
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.
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).
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
The response variable in regression or a designed experiment.
A matrix that provides the tests that are to be conducted in an experiment.
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
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.
A property of a collection of events that indicates that their union equals the sample space.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
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.
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials