Calculating PMF's and marginal PMF's problem??

[Nappy]

Hey guys,

Studying for exam here and stumbled on a problem I cant get past and need your help!

The problem deals with throwing a fair dice twice with random variables X and Y where,

X: Face value of dice on first throw
Y: Larger of two values from the 2 throws

which has joint pmf, we are looking for the conditional pmf of X given Y.

P[ X= i, Y= j] = 0 if i > j
1/36 if i < j
j/ 36 if i = j

My main problem is calculating the marginal pmf's of X and Y . I know the answers but dont understand how to get them. Also if anyone could give me a solution or help calculating the conditional pmf for Y given X it would be much appreciated...

Thanks..