first of all, these are discrete rvs hence there isn't a density
I am an engineer and hence only know basic probability etc. I request you to reply without judging me :P. Here goes my question.
I have many boxes with balls in them. X is the event that I open a random box and find that it has x balls in it. Then I add some extra balls in that box such that the number of balls in it is y.
So we have y = x + T. here T is the number of extra balls I added to that box.
My requirement is to find T as a function of x and any other constant or random variable, such that,
joint probability density p(y,x) is minimum.
I have absolutely no clue as to how I should proceed. Please give me your opinion or suggestion or advice. Thanks a lot.