% Example Monte Carlo Simulation in Matlab 
% Function: y = x2^2/x1 
% 
% Generate n samples from a normal distribution 
% r = ( randn(n,1) * sd ) + mu 
% mu : mean 
% sd : standard deviation 
% 
% Generate n samples from a uniform distribution 
% r = a + rand(n,1) * (b-a) 
% a : minimum 
% b : maximum 
n = 100000; % The number of function evaluations 
% --- Generate vectors of random inputs 
% x1 ~ Normal distribution N(mean=100,sd=5) 
% x2 ~ Uniform distribution U(a=5,b=15) 
x1 = ( randn(n,1) * 5 ) + 100; 
x2 = 5 + rand(n,1) * ( 15 - 5 ); 
% --- Run the simulation 
% Note the use of element-wise multiplication 
y = x2.^2 ./ x1; 
% --- Create a histogram of the results (50 bins) 
hist(y,50); 
% --- Calculate summary statistics 
y_mean = mean(y) 
y_std = std(y) 
y_median = median(y)