You have a function with two arguments (inputs). After that, the calculations depend on whether or not the two random variables are independent. If they are then the joint distribution is simple the product of the individual distribution. But if not, you have some serious mathematics ahead of you!
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Joint probability is the probability that two or more specific outcomes will occur in an event. An example of joint probability would be rolling a 2 and a 5 using two different dice.
Theoretical Probability.
Theoretical implies the mathematical calculation of the probability. Empirical means the actual outcomes to happen.
That's the probability that both events will happen, possibly even at the same time. I think it's called the 'joint' probability.
Empirical anything is what is observed. Theoretical is a calculation of what things ought to be.