A computer program to perform a Monte Carlo simulation of counting experiments was written. The program was based on a mathematical derivation which started with counts in a time interval. The time interval was subdivided to form a binomial distribution with no two counts in the same subinterval. Then the number of subintervals was extended to…

Through Monte Carlo procedures, three different techniques for estimating the parameter theta (proportion of the "shocks" remaining in the system) in the Integrated Moving Average (0,1,1) time-series model are compared in terms of (1) the accuracy of the estimates, (2) the independence of the estimates from the true value of theta, and…

Queuing theory is explored by considering a simple example and by simulation with a computer. Sample BASIC computer programs are included. (DT)

The purpose of this paper is to present problems (and solutions) from the areas of marketing, population planning, system reliability, and mathematics to show how a computer simulation can be used as a problem-solving strategy in probability. Examples using BASIC and two methods of generating random numbers are given. (Author/MP)

A computer program is presented which simulates the classical probability machine, using Applesoft II high-resolution graphics. Many variables are left to the user's choosing. Suggestions for using the machine, understanding the problem, the mathematical model, and further program documentation are given. (MNS)

Estimation is by means of iterative convergence to maximum likelihood estimates, and two approaches to assessing fit of the model to sample data are discussed. Relation of this general probabilistic model to other, more restricted models is explored and three cases of the general model are applied to exemplary data. (Author/RC)

Decisions to terminate training for subjects involved with discrete trial experiments in discrimination learning should utilize a probability criterion rather than a deterministic criterion. Furthermore, these decisions should be based upon the number of correct and error responses made by the subject, with the decision made to terminate training…

This paper will discuss the results of a series of computer simulations comparing the Rasch logistic model to a series of models departing to various degrees from its assumption of equal discrimination power for all items. The results have implications for test construction and test scoring, indicating how closely the conventional raw score…

Some activities designed around the Monte Carlo method of solving probability problems are described. The instructional applications of this method involve physical models or simple BASIC computer programs. (MP)

Procedures are presented for equating simultaneously several tests which have been calibrated by the Rasch Model. Three multiple test equating designs are described. A Full Matrix Design equates each test to all others. A Chain Design links tests sequentially. A Vector Design equates one test to each of the other tests. For each design, the Rasch…

A numerical procedure is outlined for obtaining an interval estimate of a parameter in an empirical Bayes estimation problem. The case where each observed value x has a binomial distribution, conditional on a parameter zeta, is the only case considered. For each x, the parameter estimated is the expected value of zeta given x. The main purpose is…

This Study Guide on Contemporary Problems, Number 8, is one of a series prepared by the American Association for the Advancement of Science representing part of the 1974-75 National Science Foundation Chautauqua-Type Short Courses for College Teachers Program. This is a test edition and contains evaluation forms to be completed by the users and to…

A computer simulation of Bayes' Theorem was conducted in order to determine the probability that an examinee was a master conditional upon his test score. The inputs were: number of mastery states assumed, test length, prior expectation of masters in the examinee population, and conditional probability of a master getting a randomly selected test…

The reliability and validity of a tailored testing procedure based on the simple logistic model was determined for an achievement test in statistics and measurement. The test was administered on a CRT terminal to students from graduate and undergraduate measurement courses. Equivalent form reliability over a one-week interval was found to be 0.595…