# Problem 44951. Verify Law of Large Numbers

Even on 27 Apr 2020
Latest activity Reply by Shuaixian on 23 Jul 2023

If a large number of fair N-sided dice are rolled, the average of the simulated rolls is likely to be close to the mean of 1,2,...N i.e. the expected value of one die. For example, the expected value of a 6-sided die is 3.5.
Given N, simulate 1e8 N-sided dice rolls by creating a vector of 1e8 uniformly distributed random integers. Return the difference between the mean of this vector and the mean of integers from 1 to N.
function dice_diff = loln(N)
A=randi([1,N],1e8,1)
M=mean(A)
B=1:N
m=mean(B)
dice_diff =abs(M-m);
end
Here is my code, but it can't work out as it needs too long time to creat A.

Shuaixian on 23 Jul 2023

Ameer Hamza on 27 Apr 2020
It works as expected
N = 6;
A = randi([1,N],1e8,1);
M = mean(A);
B = 1:N;
m = mean(B);
dice_diff = abs(M-m);
Result:
>> dice_diff
dice_diff =
1.7416e-04
The difference is 0.000174 which is the expected result. If it take a long time, you can try to use fewer random numbers.
Giuseppe Degan Di Dieco on 27 Aug 2021
Thanks Ameer for the help, easy and straightforward.
Best.
Ameer Hamza on 27 Apr 2020
I am glad to be of help.
Even on 27 Apr 2020
Thank you, I have been confused by this question for several days.
Ameer Hamza on 27 Apr 2020
Your code is correct. However, you didn't add semicolon ';' at the end of each statement. This tells MATLAB to print 1e8 number on the screen. Mathworks allocate a finite time to each solution on Cody. The display takes so long that the Cody server thinks that the is a bug in the code. Just adding a semicolon will correct the issue
function dice_diff = loln(N)
A=randi([1,N],1e8,1);
M=mean(A);
B=1:N;
m=mean(B);
dice_diff = M-m;
end
Even on 27 Apr 2020
Thank you for your answer and your patience, but it always returns wrong when I submit to the cody system.
As the requirement of this quesiton, it should be 1e8 times.