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February 11th, 2012, 04:28 PM   #1
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Rolling dice and probability law

Probability law?

We assume that we have an infinite number of 6-sided dice.
Step 1 : We start by rolling one die. The outcome is k. We recorded it by creating a random variable X(i). X(1)=k
Step 2 : We roll k dice. We sum the outcome of the k dice. So X(2) will be equal to the sum of the k rolled dice.
Step 3 : We roll the "value of X(2)" dice and so on until step n
....

Exemple :
Step 1 : I roll one die. Outcome 5. X(1)=5
Step 2 : I roll 5 dice. Outcome : 1,1,6,3,4 so X(2)=1+2+6+3+4=16
Step 3 : I roll 16 dice. Outcome : 1,1,1,2,3,3,4,4,4,5,5,5,6,6,6,6 so X(3)= 1+1+1+2+3+3+4+4+4+5+5+5+6+6+6+6=62
Step 4 : I roll 62 dice and so on until n

What is the probability law of the random variable X(i) with i=1 to n ?

Thank you for any comment.
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February 11th, 2012, 04:49 PM   #2
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Re: Rolling dice and probability law

Read problem 13 in this document, it is a beginning.

http://www.madandmoonly.com/doctormatt/ ... /dice1.pdf
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February 11th, 2012, 05:07 PM   #3
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Re: Rolling dice and probability law

Quote:
Originally Posted by wnvl
Read problem 13 in this document, it is a beginning.

http://www.madandmoonly.com/doctormatt/ ... /dice1.pdf
Thanx a lot for the document. It seems very interesting. I will read it tomorrow.
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February 12th, 2012, 07:13 AM   #4
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Re: Rolling dice and probability law

Quote:
Originally Posted by wnvl
Read problem 13 in this document, it is a beginning.

http://www.madandmoonly.com/doctormatt/ ... /dice1.pdf
I read it today.
He treated only the case X(2) computing the expect value of X(2) not the variance nor the probability law.
I was expecting more than that.
Thank you anyway.
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February 12th, 2012, 09:05 AM   #5
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Re: Rolling dice and probability law

I said it is a beginning.

Calculating the variance and the probability law for specific cases like n=2,3,4,... is not difficult.
But an exact closed formula for n in general is something else...

p.s. concerning the probability law for the case n=2, you can find it in the answer.
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