Question

How to do the monte carlo method on a calculator? step by step method.

Answer 1

A definition and general procedure for Monte Carlo simulation.

This is what we shall mean by the term Monte Carlo simulation when discussing problems in probability: Using the given data-generating mechanism (such as a coin or die) that is a model of the process you wish to understand, produce new samples of simulated data, and examine the results of those samples. That’s it in a nutshell. In some cases, it may also be appropriate to amplify this procedure with additional assumptions. This definition fits both problems in pure probability as well as problems in statistics, but in the latter case the process is called resampling. The reason that the same definition fits is that at the core of every problem in inferential statistics lies a problem in probability; that is, the procedure for handling every statistics problem is the procedure for handling a problem in probability.

The following series of steps should apply to all problems in probability. I’ll first state the procedure straight through without examples, and then show how it applies to individual examples.

Step A. Construct a simulated “universe” of cards or dice or some other randomizing mechanism whose composition is similar to the universe whose behavior we wish to describe and investigate. The term “universe” refers to the system that is relevant for a single simple event.

Step B. Specify the procedure that produces a pseudo-sample which simulates the real-life sample in which we are interested. That is, specify the procedural rules by which the sample is drawn from the simulated universe. These rules must correspond to the behavior of the real universe in which you are interested. To put it another way, the simulation procedure must produce simple experimental events with the same probabilities that the simple events have in the real world.

Step C. If several simple events must be combined into a composite event, and if the composite event was not described in the procedure in step B, describe it now.

Step D. Calculate the probability of interest from the tabulation of outcomes of the resampling trials. Now let us apply the general procedure to some examples to make it more concrete.

Here are four problems to be used as illustrations:

1. If on average 3 percent of the gizmos sent out are defective, what is the chance that there will be more than 10 defectives in a shipment of 200?
2. What are the chances of getting three or more girls in the first four children, if the probability of a female birth is 106/ 206?
3. What are the chances of Joe Hothand scoring 20 or fewer baskets in 57 shots if his long-run average is 47 percent?
4. What is the probability of two or more people in a group of 25 persons having the same birthday—i. e., the same month and same day of the month?