Generating a random number based off normal distribution in matlab

Question

I am trying to generate a random number based off of normal distribution traits that I have (mean and standard deviation). I do NOT have the Statistics and Machine Learning toolbox.

I know one way to do it would be to randomly generate a random number r from 0 to 1 and find the value that gives a probability of that random number. I can do this by entering the standard normal function

f= @(y) (1/(1*2.50663))*exp(-((y).^2)/(2*1^2))

and solving for

r=integral(f,-Inf,z)

and then extrapolating from that z-value to the final answer X with the equation

z=(X-mew)/sigma

But as far as I know, there is no matlab command that allows you to solve for x where x is the limit of an integral. Is there a way to do this, or is there a better way to randomly generate this number?

Answer 1

You can use the built-in randn function which yields random numbers pulled from a standard normal distribution with a zero mean and a standard deviation of 1. To alter this distribution, you can multiply the output of randn by your desired standard deviation and then add your desired mean.

% Define the distribution that you'd like to get
mu = 2.5;
sigma = 2.0;

% You can any size matrix of values
sz = [10000 1];

value = (randn(sz) * sigma) + mu;

%   mean(value)
%       2.4696
%
%   std(value)
%       1.9939

If you just want a single number from the distribution, you can use the no-input version of randn to yield a scalar

value = (randn * sigma) + mu;