Problem 44951. Verify Law of Large Numbers

Created by Pooja Lalan

Solve Later

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.

Solve

Solution Stats

6189 Solutions
1431 Solvers

Last Solution submitted on Jun 04, 2020

Last 200 Solutions

Problem Comments

5 Comments

5 Comments

Show 2 older comments

David Motson on 12 Nov 2019

The solution quits because it's taking too long. 1e8 is too many?

Stephen Strickland on 28 Mar 2020

The difference should essentially be zero i.e. the two averages equal. I wrote a successful script; run in my desktop environment but the tool won't accept my answer as valid.

Jasmine Bajaj on 11 Apr 2020

It crashes every time, how to complete it?

Charles Abrams on 25 Apr 2020

To get this right apparently you have to generate the random numbers exactly the same way as the answer key. When it tests your script it seeds the random number generator and then confirms whether your program gets EXACTLY the same result. However, if you generate the random numbers in any way different from the key, your answer will be "wrong" but is probably still correct.

Rafael Siqueira Telles Vieira on 2 Jun 2020 at 17:10

There is a MatLab function that does it. Nice and easy.

Solution Comments

Solution 2174463

1 Comment

1 Comment

Drake Madison on 25 Mar 2020

Note that using rand() with round() will not produce the correct answer. There is another function that must be used instead.

Solution 2167277

1 Comment

1 Comment

Belmont Aurélien on 20 Mar 2020

1e8 is too big for the Matlab website. It crashes every time I try it. I managed to find a solution on the full version so I put it in comments and cheated to pass it.

Solution 2015845

2 Comments

2 Comments

David Motson on 12 Nov 2019

I discovered using a for loop doesn't work - too slow. Then I realised that randi can generate the required vector, doh!

Gabriel Gomes on 19 Mar 2020

Can anyone do that in a size smaller than 22? That was the smallest size I could get.

Problem Recent Solvers1431

Problem Tags

rand random integers

Problem 44951. Verify Law of Large Numbers

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers1431

Suggested Problems

More from this Author13

Problem Tags

Problem 44951. Verify Law of Large Numbers

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers1431

Suggested Problems

More from this Author13

Problem Tags

Players