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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 = 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.