Monte Carlo Simulation - MATLAB Implementation

This MATLAB source code implements Monte Carlo simulation, a probability-based statistical method widely used for modeling various random phenomena such as stock price fluctuations, weather forecasting, and biological evolution. The program demonstrates how to estimate the probability of an event by generating random samples and tracking occurrence patterns through iterative simulations. %% Monte Carlo Simulation Source Code clear; clc; % Define simulation parameters n = 1000; % Number of simulation iterations a = 0; % Lower bound of simulation range b = 1; % Upper bound of simulation range % Initialize counter variable count = 0; % Tracks successful events meeting criteria % Begin Monte Carlo simulation loop for i = 1:n x = a + (b-a)*rand(); % Generate uniform random number in [a,b] range if x^2 < 0.5 % Check if generated value meets condition (example: falling within curve y=x^2 below 0.5) count = count + 1; % Increment counter for successful events end end % Calculate empirical probability prob = count/n; % Probability = successful events / total trials % Display results disp(['Estimated probability of event occurrence: ', num2str(prob)]); Key implementation details: - Uses MATLAB's rand() function for uniform random number generation - Implements basic Monte Carlo algorithm through iterative sampling - Demonstrates probability estimation via frequency counting approach - Clear separation of parameter definition, simulation loop, and result calculation phases