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.

Therandnfunction returns a sample of random numbers from a normal distribution with mean 0 and variance 1. The general theory of random variables states that ifxis a random variable whose mean is $${\mu }_x$$and variance is $${\sigma }_x^2$$, then the random variable,y, defined by $$y=ax+b,$$whereaandbare 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.

= 5;b = 500;y =。* randn (1000 1) + b;

Calculate the sample mean, standard deviation, and variance.

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

stats =1×3499.8368 4.9948 24.9483

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

See Also

rng|randn

Related Topics

• Random Numbers Within a Specific Range
• Random Numbers Within a Sphere
• Create Arrays of Random Numbers