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February 11th, 2012, 04:28 PM  #1 
Senior Member Joined: Jan 2011 Posts: 560 Thanks: 1  Rolling dice and probability law
Probability law? We assume that we have an infinite number of 6sided 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. 
February 11th, 2012, 04:49 PM  #2 
Senior Member Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0  Re: Rolling dice and probability law
Read problem 13 in this document, it is a beginning. http://www.madandmoonly.com/doctormatt/ ... /dice1.pdf 
February 11th, 2012, 05:07 PM  #3  
Senior Member Joined: Jan 2011 Posts: 560 Thanks: 1  Re: Rolling dice and probability law Quote:
 
February 12th, 2012, 07:13 AM  #4  
Senior Member Joined: Jan 2011 Posts: 560 Thanks: 1  Re: Rolling dice and probability law Quote:
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.  
February 12th, 2012, 09:05 AM  #5 
Senior Member Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0  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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