Question

2. Generate a large number of Gaussian distributed random numbers with mean 0 and variance 1. (HINT: use the randn command) a) Provide a scatter plot of the random numbers b) Plot the pdf of the distribution (similar to 1) and compare with theoretical pdf given in the class handout. c) If I want to generate a Gaussian distributed random numbers with mean 2 and variance 9 from the previously generated set of random numbers, how would I do it? d) Perform part (c) and plot the pdf for the new random variable.

Answer 1

MATLAB Code:

close all
clear
clc

x = randn(1,10000);
figure, scatter(1:10000, x), title('Scatter Plot'), grid
xlabel('Sample Index'), ylabel('Sample Value')

figure, hist(x, 1000), title('PDF (Mean = 0, Variance = 1)')
grid
% As can be seen from the pdf, the mean = 0.

var = 9; std = sqrt(var);
mean = 2;
y = std*x + mean; % Generating random numbers with specified mean and variance
figure, hist(y, 1000), title('PDF (Mean = 2, Variance = 9)')
grid

Plots:

MATLAB Code: close all clear clc x = randn(1,10000): figure, scatter(1: 10000, x), title(�Scatter Plot'), grid xlabel(�Sample Index'), ylabel(�Sample Value') figure, hist(x, 1000), title(�PDF (Mean = 0, Variance = 1)') grid % As can be seen from the pdf, the mean = 0. var = 9: std = squareroot (var): mean = 2: y = std*x + mean: % Generating random numbers with specified mean and variance figure, hist(y, 1000), title(�PDF (Mean = 2, Variance = 9)') grid Plots: PDF (Mean = 0, Variance = 1) PDF (Mean = 2, Variance = 9)