i am working with a set of distributions. I have so far analyzed several probability distributions with respect to each other, that means i have made a t-test, to see how probable it is that two events happen at the same time according to those distributions. That means i have computed:
let x1 and x2 be probability distributions prob(x1=Z, x2=Z), z be any value
thats what the t-test gave me. though i used something similar so the distributions can have different variances. I have now computed the overlap of both distributions with respect to each other.
what i want to do now is look at the whole thing backwards. I want to look at a certain range and be able to give a probability that there is 1 or two of those occurrences. perhaps another way to look at it is using dice. I have two dice with differing probability distributions (probably gaussian for me, but lets assume one throws 6 more often, the other one 3 more often). The first way to look at it would be to tell whether both dice throw the same number. What i want to do is to tell if both dice throw a number in a certain range, for example 5 and 6.
let x1 and x2 be probability distributions prob(x1=Z, x2=Z), z be a value a certain range
I think it would help if you could tell me what the name of the thing is that i am trying to do, so i can read up. But i would also be happy to have a solution that works out of the box.
any pointers how i can compute this?
cheers and thanks for advice
edit: provided an example.