- 12.4.1: Prove that the formula in Eq. (12.4.1) is the same as importance sa...
- 12.4.2: Let g be a function, and suppose that we wish to compute the mean o...
- 12.4.3: Let Y have the F distribution with m and n degrees of freedom. We w...
- 12.4.4: We would like to calculate the integral 0 log(1 + x) exp(x) dx. a. ...
- 12.4.5: Let U have the uniform distribution on the interval [0, 1]. Show th...
- 12.4.6: . Suppose that we wish to estimate the integral 1 x2 2 e0.5x2 dx. I...
- 12.4.7: Let (X1, X2) have the bivariate normal distribution with both means...
- 12.4.8: . Suppose that we wish to approximate the integral g(x) dx. Suppose...
- 12.4.9: . Let F be a continuous strictly increasing c.d.f. with p.d.f. f . ...
- 12.4.10: For the situation described in Exercise 6, use stratified importanc...
- 12.4.11: . In the notation used to develop stratified importance sampling, p...
- 12.4.12: Consider again the situation described in Exercise 15 of Sec. 12.2....
- 12.4.13: The method of control variates is a technique for reducing the vari...
- 12.4.14: Suppose that we wish to integrate the same function g(x) as in Exam...
- 12.4.15: The method of antithetic variates is a technique for reducing the v...
- 12.4.16: Use the method of antithetic variates that was described in Exercis...
- 12.4.17: For each of the exercises in this section that requires a simulatio...
Solutions for Chapter 12.4: Simulation
Full solutions for Probability and Statistics | 4th Edition
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
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.
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
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 mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
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.
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
The amount of variability exhibited by data
Error mean square
The error sum of squares divided by its number of degrees of freedom.
A subset of a sample space.
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.
Exponential random variable
A series of tests in which changes are made to the system under study
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.