Problem 44951. Verify Law of Large Numbers

Created by Pooja Lalan

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>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</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>3.5</w:t></w:r><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>N</w:t></w:r><w:r><w:t>, simulate</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>1e8</w:t></w:r><w:r><w:t> N-sided dice rolls by creating a vector of</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>1e8</w:t></w:r><w:r><w:t> uniformly distributed random integers. Return the difference between the mean of this vector and the mean of integers from</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>1</w:t></w:r><w:r><w:t> to</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>N</w:t></w:r><w:r><w:t>.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

27018 Solutions
6792 Solvers

Last Solution submitted on Oct 02, 2022

Last 200 Solutions

Problem Comments

16 Comments

16 Comments

Show 13 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 S.T. Vieira on 2 Jun 2020

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

Louis Repussard on 9 Oct 2020

Nice one

Wooseong Choi on 25 Oct 2020

"1e8 N-sided dice" made me confused. I think it should be changed to "1e8-sided dice".

Ryan Chapman on 27 Nov 2020

this problem brakes the website. 1e8 is too big and the website blocks out my computer.

Victor Zarate on 11 Feb 2021

After multiple tries of submitting what i thought the correct answer and being met with "While evaluating the solution, the server encountered an error caused by temporary unavailability of MATLAB Service. Wait a few minutes for the MATLAB Service to return, and then rescore." what seemed to do the trick was what Marcel Dornbusch hinted in his comment.
Just make sure you do not output every bit of information in the code, and just output the answer.

Glitta Rosalia on 31 May 2021

description of this problem is confusing.

Isabella Stellitano on 14 Nov 2021

Good problem

Johain Faraj on 28 Dec 2021

nice problem

饶城饶 on 1 Apr 2022

description of this problem is confusing.

dang dong on 17 Apr 2022

nice

Ifte on 11 Jul 2022

Challenging to make small!

士元梁 on 13 Jul 2022

quite a good question.
i think that makes meaning in statistics.

Solution Comments

Solution 8532980

1 Comment

1 Comment

migue ange cc on 13 Jun 2022

Need to read more carefully.

Solution 8428305

1 Comment

1 Comment

鹏飞范 on 21 May 2022

the question is confusing

Solution 8050260

1 Comment

1 Comment

Bryan Mutinda on 21 Apr 2022

please improve how the question is asked. It is unclear and takes a while to understand the question however, once understood the code to do it is easy

Solution 6970664

1 Comment

1 Comment

Haoran Tian on 26 Nov 2021

hard one

Solution 6930984

1 Comment

1 Comment

Josh Klueber on 21 Nov 2021

easy

Solution 6736543

1 Comment

1 Comment

Romain Dodet on 20 Oct 2021

I passed with a bullsh$t code

Solution 6112298

1 Comment

1 Comment

Furkan Atak on 15 Jul 2021

You roll N-sided dice 1e8 times. It takes a while for me to get this. Apart from it an easy question.

Solution 5311217

Solution 5164663

1 Comment

1 Comment

Maya Gonzalez on 24 Mar 2021

this one is fun!

Solution 5162063

1 Comment

1 Comment

Manfred Neumann on 24 Mar 2021

It's really confusing, but: you have a dice with N sides! and you roll this dice 1e8 times!
Since I checkt this, the solution was clear ...

Solution 5024526

2 Comments

2 Comments

李君 on 9 Mar 2021

description of this problem is confusing.

Nilver Torres Romani on 10 Jan 2022

that's right :(

Solution 4569343

1 Comment

1 Comment

Sandor Szabo on 10 Jan 2021

Incorrect!
I created a "step by step" solution that was not accepted. Then I reformulated this solution for compound formula end, voila, it was accepted.

Solution 4564648

1 Comment

1 Comment

Alain Daniel Godo Alonso on 9 Jan 2021

I don't know why every time I send the solution the site show me: "While evaluating the solution, the server encountered an error caused by temporary unavailability of MATLAB Service. Wait a few minutes for the MATLAB Service to return, and then rescore."

Solution 4528718

Solution 3960703

Solution 3774598

1 Comment

1 Comment

Lester Goh on 22 Nov 2020

why tho

Solution 2636518

1 Comment

1 Comment

Marcel Dornbusch on 30 Jun 2020

For saving execution time, do without outpout! Then it worked for me.

Solution 2504012

1 Comment

1 Comment

AIJAZ BHAT on 9 Jun 2020

what is the problem with this solution

Solution 2174463

2 Comments

2 Comments

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.

Grey Bohr on 3 Jul 2020

What can be used? I am a bit confused.

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 Solvers6792

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 44951. Verify Law of Large Numbers

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers6792

Suggested Problems

More from this Author13

Problem Tags

Community Treasure Hunt

Problem 44951. Verify Law of Large Numbers

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers6792

Suggested Problems

More from this Author13

Problem Tags

Community Treasure Hunt

Players