I have a question about creating a probability distribution.:
Let's say we have two sets of events with five elements (real numbers) and two random variables X and Y. So, we have one set for each random variable.
In this case, we assign given probabilities to events from these sets.
I am given the following question "find the probability distribution of XY."
Could you explain me what steps I should take in doing this? I tried to multiply each event from X with each event from the other set to find XY and tried to compute the probabilities for each of the 25 events by multiplying the ones from the set of X with the ones from set of Y. However, I was not successful, and I got a total probability over 1. Does this sound too awful? Did I make a mistake here?
I will be really glad, if you could help me to understand what the question means formally and what I should be doing in this situation.