Random Numbers from Normal Distribution with Specific Mean and Variance

This example shows how to create an array of random floating-point numbers that are drawn from a normal distribution having a mean of 500 and variance of 25.

The randn function returns a sample of random numbers from a normal distribution with mean 0 and variance 1. The general theory of random variables states that if x is a random variable whose mean is $${\mu }_x$$ and variance is $${\sigma }_x^2$$, then the random variable, y, defined by $$y=ax+b,$$where a and b are constants, has mean $${\mu }_y=a{\mu }_x+b$$ and variance $${\sigma }_y^2=a^2{\sigma }_x^2.$$ You can apply this concept to get a sample of normally distributed random numbers with mean 500 and variance 25.

First, initialize the random number generator to make the results in this example repeatable.

rng(0,'twister');

Create a vector of 1000 random values drawn from a normal distribution with a mean of 500 and a standard deviation of 5.

a = 5;
b = 500;
y = a.*randn(1000,1) + b;

Calculate the sample mean, standard deviation, and variance.

stats = [mean(y) std(y) var(y)]

stats = 1×3

  499.8368    4.9948   24.9483

The mean and variance are not 500 and 25 exactly because they are calculated from a sampling of the distribution.