Let us say, we have two random variables, x1 --> U(10,20) i.e. x1 is uniformly distributed between 10 and 20, and x2 --> U(20,40) i.e. x2 is uniformly distributed between 20 and 40.
Moreover, it has to be ensured that x1+x2 = 40 always.
How do I compute the joint distribution P(X1,X2|X1+X2=40)?
In other words, how do I find joint distribution based on a sum constraint?