Dalhousie University

• STAT 2060

• Stat 2060 - Joint Probability Distribution Lecture Notes – Chapter 5 Dr. Ammar Sarhan Department of Mathematics & Statistics, Dalhousie University November 2, 2016 Dr. Ammar Sarhan Joint Probability Distribution November 2, 2016 1 / 24 5.1 Joint distribution function Let X and Y be two discrete rv’s defined on the sample space S of an experiment. The joint probability mass function (pmf), p(x, y), is defined for each pair (x, y) by p(x, y) = P{X = x, Y = y} The joint pmf satisfies the following: 1 p(x, y) ≥ 0 for every (x, y) 2 P x P y p(x, y) = 1 Let A = {(x, y) : x ∈ {x1, · · · , xn}, y ∈ {y1, · · · , ym}} be an event consisting of pairs of (x, y) values, then P(A) = X X (x,y)∈A p(x, y