9.1: MATLAB Random Number Functions

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Carey Smith
Oxnard College

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By Carey A. Smith

The code in this section is in the file: MATLAB_Random_Number_Functions.m

Random numbers are useful in MATLAB simulations of real-world signals and events which have uncertainty. There are 3 main MATLAB random number generators:

randi(IMAX,M,N) Random Integers

RndInt = randi(IMAX,M,N) returns an M-by-N matrix of uniformly distributed pseudo-random integers from 1 to IMAX.

Example 1A: Generate a vector of 8 dice rolls:

Dice = randi(6,1,8)

Example 1B: Generate a 4x3 array of random integers between 0 and 100

RndInt_4_3 = randi(100,4,3)

rand(M,N) Random Decimals

RndDec = rand(M,N) returns an M-by-N matrix of uniformly distributed pseudo-random decimal numbers between 0 and 1.

Example 2A: Generate 8 random decimals between 0 and 1:

RndDec2A = rand(1,8)

The vector can be scaled to be between any 2 numbers by adding an offset number and multiplying by a scale factor.

Example 2B: Generate 8 random decimals between –1 and 1:

RndDec2B = 2*rand(1,8) - 1

randn(M,N) Normally Distributed Random Numbers

RndNorm = randn(M,N) returns an M-by-N matrix of pseudo-random values drawn from the standard normal distribution, which has a mean (average) = 0 and a standard deviation = 1.

The standard deviation is a measure of the spread of the data. For a further explanation, watch this video:

“Standard Deviation - Explained and Visualized”, by Jeremy Blitz-Jones

https://www.youtube.com/watch?v=MRqtXL2WX2M

The Normal Distribution is also called the “Gaussian Distribution”.

Example 3A:

RndNorm3A = randn(1,5)

The result can be scaled to have any mean and standard deviation by adding an offset number and multiply by a scale factor.

Example 3B: Generate random pulse rates with a mean = 90 and a standard deviation of 15:

Pulse_rates = 90 + 15* randn(1,5)

Example 3C: A radar signal has magnitude 20 with noise of magnitude = 4 (standard deviation)

Received_signal = 20 + 4*randn(1,5)

Figure \(\PageIndex{1}\): Standard Normal Probability Distribution

The total area under the curve = 1.00. Approximately:

68% is between -1 and +1 standard deviations

95% is between -2 and +2 standard deviations

99.7% is between -3 and +3 standard deviations

The normal distribution approximates many things, such as:

Noise in signals
Measurement errors
Clinical trials of medicines and vaccines
Probability and statistics
Biological data, such as weights, heights, pulse rates, blood pressure, diabetes, etc.

The “Central Limit Theorem” states that the sum or average of random variables becomes normal as the number of data (the sample size) increases, even if the raw data is not normally distributed.

You may want to watch Mike’s Galton Machine video. It uses ball bearings to build up a normal distribution: https://www.youtube.com/watch?v=VQepRP-f6GA

The Standard Normal Probability Distribution plot can be created with this code:

% NormalDistribution.m

x = -4:0.01:4;

mu = 0; % mean

std_dev = 1; % standard deviation

y = (1/(std_dev*sqrt(2*pi))) * exp((-1/2)*((x-mu)/std_dev).^2);

figure;

plot(x,y,'LineWidth',4)

grid on;

title('Standard Normal Distribution','FontSize',14)

xlabel('Number of Standard Deviations','FontSize',12)

ax = gca

ax.LineWidth = 2