# Monte Carlo Integration & Acceptance Rejection Method

Monte Carlo Integration & Acceptance Rejection Method Problems

a. Use the Monte Carlo Method to numerically integrate the following function (run at least 500,000 trials). Show the number of "hits" using a forecast display, calculate the hit/total ratio and finally the numerical value of the integral

(see attached for formula)

b. Use the Acceptance//Rejection Method to generate values of a Random Variable which have the following Probability Distribution:

(see attached for formula)

https://brainmass.com/math/fractions-and-percentages/monte-carlo-integration-acceptance-rejection-method-547890

#### Solution Preview

Please see the attached files for the solution.

I hope this helps!

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Problem a

The first tab of the attached Excel file includes the solution to this problem. Note that, due to file size issues, only 100,000 trials were run (instead of 500,000). Once you download the file, this issue can be easily fixed by creating more rows beyond the 100,000th one using the same formulas as for the previous ones. The result, given in cell H4, will take into account these additional cells when created.

The integration was done as follows:

First, note that the maximum possible value of the probability distribution function must be 4. The function is strictly decreasing in x, ...

#### Solution Summary

Monte Carlo integration and acceptance rejection methods are discussed.