- 12.7.1: Test the standard normal pseudo-random number generator on your com...
- 12.7.2: Test the gamma pseudo-random number generator on your computer. Sim...
- 12.7.3: Test the t pseudo-random number generator on your computer. Simulat...
- 12.7.4: Let X and Y be independent random variables with X having the t dis...
- 12.7.5: Consider the power calculation done in Example 9.5.5. a. Simulate v...
- 12.7.6: The 2 goodness-of-fit test (see Chapter 10) is based on an asymptot...
- 12.7.7: In Sec. 10.2, we discussed 2 goodness-of-fit tests for composite hy...
- 12.7.8: In Example 12.5.6, we used a hierarchical model. In that model, the...
- 12.7.9: In Example 12.5.6, we modeled the parameters 1,..., p as i.i.d. hav...
- 12.7.10: Let X1,...,Xk be independent random variables such that Xi has the ...
- 12.7.11: 852 Chapter 12 Simulation c. Use simulation to assess the approxima...
- 12.7.12: Consider again the situation described in Exercise 11. This time, u...
- 12.7.13: Suppose that our data comprise a set of pairs (Yi, xi), for i = 1,....
- 12.7.14: Use the simulation scheme developed in Exercise 13 and the data in ...
- 12.7.15: In Sec. 7.4, we introduced Bayes estimators. For simple loss functi...
- 12.7.16: In Example 12.5.2, suppose that the State of New Mexico wishes to e...
Solutions for Chapter 12.7: Simulation
Full solutions for Probability and Statistics | 4th Edition
a-error (or a-risk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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.
A distribution with two modes
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
The variance of the conditional probability distribution of a random variable.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
Another term for the conidence coeficient.
A probability distribution for a continuous random variable.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
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 hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
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.
The amount of variability exhibited by data
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
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.
In statistical quality control, that portion of a number of units or the output of a process that is defective.