Question

Use a random number generator to produce 1000 uniformly distributed numbers with a mean of 10, a minimum of 2, and a maximum of 18. Obtain the mean and the histogram of these numbers, and discuss whether they appear uniformly distributed with the desired mean.

Answer 1

We need to generate the 1000 uniformly distributed random numbers with minimum of 2 and maximum of 18. Then we need to check it by plotting histogram.

In MATLAB, the function rand(m, n) generates uniformly distributed random numbers between 0 and 1. Now, since we need an array of 1000 numbers, in our case m = 1 and n = 1000. Also, we need minimum value of 2. That can be achieved by adding 2 to the array created. Then we need maximum value of 18. That can be achieved by multiplying the difference i.e. 16 to the array created. Therefore, the formula for getting the a uniformly distributed number in interval [a, b] is:

(b – z)y + a

 

Where

y is the random number generated

 

The MATLAB code is shown below:

 

Input:

a = 2;

b = 18;

y = (b-a)*rand(1, 1000) + a;

mean(y)

hist(y, 16)

We have also checked the array generated by calculating mean and the histogram

 

Output:

ans =

10.1841

 

We see that the mean is 10.1814, which is very close to the mean of 10 in question.

 

The histogram is shown below:

 

Histogram is shows that all the bins are nearly of equal length with slight variations. Hence, this can be approximated as a uniform distribution.

We see that the mean is 10.1814, which is very close to the mean of 10 in question.