Statistics Help-Joint pmf and marginal pmfs

[runner4life]

Statistics Help--Joint pmf and marginal pmfs

Homework Statement

Let X1 and X2 be iid discrete uniform random variables with support on the integers {1,2,3,...,n}.

Find the joint pmf of Y=max(X1,X2) and W=min(X1, X2).
Find the marginal pmf's of W and Y

Homework Equations

The Attempt at a Solution

I need help on how to set this problem up. the max and min is throwing me off.

 

[lanedance]

so imagine the variables as forming a 2D lattice, each of the lattice points having equal probability

as always consdier a few cases to get going
max(x1,x2) = 1, can only be (1,1)
max(x1,x2) = 2, can be (2,1), (2,2), (1,2)
max(x1,x2) = 3, can be (3,1), (3,2) (3,3), (3,1), (3,2)

this form should give you a hint on how to work out a generic formula

to understand why this formula works, try plotting the points on your lattic & see where they fall