I am working on a physical random number generator that is hopefully can generate RN with arbitrary distribution. I am trying to research some applications for this RNG. I have some basic question about Monte Carlo as below:
For example, if I have two correlated events, one has probability distribution A, the other has probability distribution B. These two events are correlated according to a joint probability distribution AB. I want to apply Monte Carlo simulation. I know I need to generate correlated random numbers to run the simulation. Please tell me which step is correct:
a. Do I need to generate independent random numbers for each event with probability dist. A and B separately.
b. When I choose a proper joint density function to generate correlated random numbers, is this true that I only have some known pdf that I can choose from to fit my data the most (such as normal, log normal, sinh-1 , etc.) If it’s true, if I can have a way to generate correlated random numbers with arbitrary pdf, will it be very helpful for Monte Carlo simulation?? Thank you.