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June 23rd, 2012, 09:51 AM  #1 
Newbie Joined: Jun 2012 Posts: 1 Thanks: 0  Combining 2 data sets
Sorry the title is ambiguous but I don't know what one would call these types of data sets. The situation is effectively this: There is a 10 sided weighted die which 2 people have rolled. For one person it is impossible for them to roll 1 or 2, for another person it is impossible to roll 3 or 4 however the weights of 510 are constant on both dice. I have frequency data submitted by each person, the reason behind combining them is to firstly get a better idea of the relative weights of 510, and secondly to see the weights of 14 in one set. 
August 10th, 2012, 03:32 AM  #2 
Senior Member Joined: Aug 2012 Posts: 229 Thanks: 3  Re: Combining 2 data sets
Hey Shakarii. You can create a random variable by taking the cartesian product of both random variables A X B Where A is the state space for 1st player and B is for 2nd player. You then have to define your random variable as a function of the two: for example the sum of the two rolls would be X = A + B. Since both rolls are independent we know that P(A and B) = P(A)P(B) (we assume independence to make things easier). Then if we want to find moments we use expectation formulas over the two variables. If you want the probability distribution for X = A + B (i.e. PDF of X) then you need to use what is called a Probability Generating Function. Have you come across this? 

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