please help

[kim270]

two fair dice are rolled. find the joint probability mass function of X and Y when X is the largest value obtained on any die and Y is the sum of the values

im a little confused on how i could find each individual probability to get the mass function

 

[pka]

First, lets clear the meaning. If we roll (1,1) then X=1 and Y=2.
Rolling (4,2) we get X=4 and Y=6.
Thus X has values: 1, 2, 3, …,6; Y has values: 2, 3, 4,…,11, 12.
The event (X=1,Y=2) happens in only one way.
The event (X=4,Y=7) happens in only one way.
The event (X=5,Y=2) CANNOT happen.
So how many elementary events are there?
Then what is the probability of each?