How to generate random numbers from a normal distribution with specific mean and variance?

Question

I need to generate a Gaussian random sample of n numbers, with mean 0 and variance 1, using the randn function.

In general, how would I generate a Gaussian random sample X of n numbers, with mean mu and variance v, using the randn function?

Solution 1

A standard normal distribution already has mean 0 and variance 1.

If you want to change the mean, just "translate" the distribution, i.e., add your mean value to each generated number. Similarly, if you want to change the variance, just "scale" the distribution, i.e., multiply all your numbers by sqrt(v). For example,

v = 1.5; % variance
sigma = sqrt(v); % standard deviation
mu = 2; % mean
n = 1000
X = sigma .* randn(n, 1) + mu;
stats = [mean(X) std(X) var(X)]

See the following article:

https://ch.mathworks.com/help/matlab/math/random-numbers-with-specific-mean-and-variance.html

for more info.

Solution 2

You could also call

normrnd(0,1,[M,N])

or

random('Normal',0,1,[M,N])