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Consider n loaded dice with differing probability distributions. I have constructed an equation that tells me the probability mass, the number of times a certain number is expected to be thrown.

Now i want to extend the numerical range from a line onto a plane. How do i get the expected number of times a number/number combination is thrown now?

The two dicerolls are independent. Can i compute the probability mass for the combination using my equation for computing the probability mass for the line? Since the probability mass is not a probability i cannot just multiply those. What will i have to change?

Thanks for the advice

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It is unclear what you are asking; are there two dice or $n$, or are you rolling $n$ dice two times? –  Josh Guffin Nov 6 '10 at 14:57
    
I am rolling n dice in pairs. once for the x-coordinate and once for the y coordinate.what i am interested in is the probability mass on the plane. –  tarrasch Nov 8 '10 at 9:46
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up vote 3 down vote accepted

What you want is called the "Joint Distribution Function" of the dice. That is, for two dice with random variables $X$ and $Y$ measuring the number showing on the faces, it is $P(X=x,Y=y)$. Since the dice are independent, the JDF is the product of the individual distribution functions of $X$ and $Y$ (what you call the mass function): $$P(X=x,Y=y) = P(X=x)P(Y=y).$$

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