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June 23rd, 2012, 09:51 AM   #1
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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 5-10 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 5-10, and secondly to see the weights of 1-4 in one set.
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August 10th, 2012, 03:32 AM   #2
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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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