Norm (not standard normal) random variable?

How to generate using Gauss command for a normal distribution with any mean and variance?

2 Answers


To compute random numbers which are normally distributed with a mean mu and variance sigma, you multiply the result of rndn by the square root of sigma and adding mu like this:

// Mean of random numbers
mu = 8.2;

// Variance of random numbers
sigma2 = 5.4;

// Number of observations to create
nobs = 1e6;

// Create random numbers N(mu, sigma2)
X = rndn(nobs, 1) * sqrt(sigma2) + mu;

print meanc(X);
print varCovXs(X);

The above code should create random normal numbers with a mean near 8.2 and a variance near 5.4. If you want to be able to make some reusable code, you could create a procedure like this:

x = rndn2(100, 1, 0.5, 1.4);

proc (1) = rndn2(nobs, c, mu, sigma2);
    retp(rndn(nobs, c) * sqrt(sigma2) + mu);


Thanks. Where does the “mu “ enter into this command in your first code? I cannot see anything after “sig”.

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