The discussion revolves around the joint moment generating function of two random variables, X and Y, represented as MXY(s,t) = 1/(1-2s-3t+6st) for specified conditions on s and t. Participants are tasked with finding probabilities related to the minimum and maximum of X and Y.
The discussion includes attempts to verify the factorization of the joint moment generating function. Some participants express uncertainty about the correctness of their proposed forms, indicating an ongoing exploration of the problem.
Participants are working under the constraints of the joint moment generating function's conditions and are exploring the implications of these constraints on their calculations.
wannabe92 said:Hi, I've no idea where to go with the question below:
Joint moment generating function of X and Y - MXY(s,t) = 1/(1-2s-3t+6st)
for s<1/2, t<1/3.
Find P(min(X,Y) > 0.95) and P(max(X,Y) > 0.8)
Ray Vickson said:Can you represent M_{XY}(s,t) in the form M_1(s) \cdot M_2(t)?
RGV
wannabe92 said:Is it 1/(1-2s) . 1/(1-3t)?