monte carlo simulation in matlab

Monte Carlo simulation is a computational technique used to study and solve mathematical problems that include random variables. It involves using randomly generated numbers to simulate real-life scenarios in order to estimate the outcome of a situation.

Here is an example of how to perform a Monte Carlo simulation in MATLAB, using a for loop and a random number generator:

main.m
% Define variables
n = 1000; % number of simulations
a = 1; % lower bound of range
b = 10; % upper bound of range

% Initialize storage for results
results = zeros(n,1);

% Perform Monte Carlo simulation
for i = 1:n
    % Generate random number between a and b
    x = a + (b-a)*rand();
    
    % Store result
    results(i) = x^2;
end

% Compute mean, standard deviation, and plot results
mean_results = mean(results);
std_results = std(results);
histogram(results, 20);
title(['Monte Carlo Simulation Results: Mean = ', num2str(mean_results), ', SD = ', num2str(std_results)]);
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In this example, the code performs a Monte Carlo simulation to estimate the outcome of the function x^2 using 1000 simulations. The results are stored in a results array, which is then used to compute the mean and standard deviation of the simulated values. The histogram function is used to plot the results of the simulation.

Note that the key part of the code is the for loop, which generates a random value for x using the rand function, and then stores the result of x^2 in the results array. By repeating this process many times, we can get a sense of the distribution of possible outcomes for the function x^2.