monte carlo in matlab

Monte Carlo simulation is a widely used method for solving various problems by generating random samples repeatedly. The following steps show how to perform Monte Carlo simulations in MATLAB:

1. Set up the problem: Determine the problem to be solved and define the relevant variables and their ranges.

2. Generate random numbers: Use a random number generator to generate random numbers in the specified ranges.

main.m
% generating random numbers
n = 1000; % number of random samples
x = rand(n,1); % generate uniformly distributed random numbers (between 0 and 1)
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3. Transform the random numbers to the desired range and distribution. This step is optional and not applicable to all problems.

main.m
% transform uniformly distributed random numbers to normal distribution
mu = 5; sigma = 2;
y = mu + sigma*randn(n,1); 
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4. Evaluate the function for each set of generated random numbers.

main.m
% evaluate a function for each set of random numbers
f = x.^2; % evaluating the function y = x^2
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5. Calculate the statistical measures of interest, such as the mean and standard deviation.

main.m
% calculate the mean and standard deviation
mean_f = mean(f);
std_f = std(f);
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6. Visualize the results, if necessary.

main.m
% visualize the distribution of the function values
histogram(f);
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By repeating these steps with different random seeds, more accurate estimates of the statistical measures can be obtained. Monte Carlo simulation is very useful in many fields, including finance, physics, and engineering, among others.