How to generate 100,000 random samples (1D) from 2 PDFs?

Question

Can anyone help me how to write a MATLAB code to generate 100,000 random samples (1D)?

The samples should follow 2 PDFs:

1. N(+1, 0.5)
2. N(-1, 0.5)

where the notation N(µ,σ) indicates a Normal distribution with mean µ and standard deviation σ.

Answer 1

Use the randn() function and substitute in mean and standard deviation as follows

mu + stdev.*randn(100,1)

For more information, check out the matlab help for randn()

http://www.mathworks.com/help/matlab/ref/randn.html

Answer 2

Alternatively, you can use MATLAB's Probability Distribution Objects which make working with probability distributions very easy.

Note this solution requires the Statistics and Machine Learning Toolbox to use makedist() and random().

% MATLAB R2018b
% Define probability distribution objects
pd1 = makedist('Normal',1,0.5');
pd2 = makedist('Normal',-1,0.5');
% Generate Samples
X1 = random(pd1,100,1);
X2 = random(pd2,100,1);