Question

Use a random number generator to produce 1000 normally distributed numbers with a mean of 20 and a variance of 4. Obtain the mean, variance, and histogram of these numbers, and discuss whether they appear normally distributed with the desired mean and variance.

Answer 1

Program plan:

• To find the mean and variance of the 1000 normally distributed random numbers.

• To plot the histogram of these random numbers.

 

Program:

%**********************************************************

%A matlab code is written to find the mean and variance of

%the normally distributed random number with mean 20 and

%variance 4. To obtain the histogram of the numbers using

%matlab.

%**********************************************************

%Declaration of constant

m=1000;

%Generates 1000 random number of mean 20 and variance 2

x=2.*randn(1,m)+20;

%Displays text

disp('The mean of the 1000 random number is ');

%Displays value

disp(mean(x));

%Displays text

disp('The variance of the random numbers is ');

%Displays value

disp((std(x))^2);

%Declaration of array

range=[min(x):max(x)];

%Creates histogram

hist(x, range),

%Assigns text to x-axis

xlabel('Random values'),

%Assigns text to y-axis

ylabel('Absolute Frequency')

 

Output:

>> Untitled

The mean of the 1000 random number is

20.1020

 

The variance of the random numbers is

4.2016

The mean of the 1000 random number is

20.1020

 

The variance of the random numbers is

4.2016