Discussion Problem_ (6)

Posted by duck on Apr 12, 2013; 2:33pm
URL: http://discussion-forum.276.s1.nabble.com/Discussion-Problem-6-tp7580047.html

Q1) Consider two random variables X and Y, each taking values in {1, 2, 3}. Let their joint PMF be such that for any 1 ≤ x, y ≤ 3,
Pr (X = x, Y = y) = f(x, y) = 0,  if (x, y) ∈ {(1, 3), (2, 1), (3, 2)}
Pr (X = x, Y = y) = f(x, y) > 0,  otherwise
Then,
(i) X and Y can be independent or dependent depending upon the strictly positive values.
(ii) X and Y are always independent.
(iii) X and Y can never be independent.