A balanced die is tossed twice Let X and Y denote the smalle

A balanced die is tossed twice. Let X and Y denote the smaller and larger of the faces, respectively.

a) Find the joint PMF of X and Y

Solution

X is the smaller face and y is the larger face

Sample space

(x,y) = (1,2)(1,3)(1,4)(1,5)(1,6)

          (2,3)(2,4)(2,5)(2,6)

         (3,4)(3,5)(3,6)

         (4,5)(4,6)

         (5,6)

There are 15 elements in the sampe space.

If total prob is equal to 1, then each has prob as 1/15

Thus joint pmf of x,y is

=1/15, x>y

=0 otherwise.