Suppose X and Y are discrete rvs such that PXY1 This means t

Suppose X and Y are discrete r.v.s. such that P(X=Y)=1. This means that X and Y always take on the same value.

a) Do X and Y have the same PMF?

b) Is it possible for X and Y to be independent?

Solution

a) yes because it says that x and y always take on the same value

b) no because as you can see in the problem

P(x=y) = 1

that says that x and y ALWAYS take on the same value so x and y are dependent.

it is not possible that x and y to be independent