The joint probability mass function of PfracXY 1 PXY2 PXY

The joint probability mass function of P(frac{X}{Y} > 1) = P(XY=2) = P(X+Y>4) = begin{array}{lll} p(1,1) = 0.3 & p(1,2) = 0.1 & p(1,3) = 0.1 cr p(2,1) = 0.1 & p(2,2) = 0.1 & p(2,3) = 0.1 cr p(3,1) = 0.1 & p(3,2) = 0.1 & p(3,3) = 0 end{array} Compute the following probabilities: Y is given by X and

Solution

P(X + y) > 4 = 0.1 + 0.1 + 0 = 0.2 (this is at (3,2), (2,3), and (3,3); 2+3, 3+2, and 3+3 are greater than 4)

P(XY = 2) = 0.1 + 0.1 = 0.2 (this is at (2,1) and (1,2), 1*2 and 2*1 equal 2)

P(X/Y > 1) = 0.1 + 0.1 + 0.1 = 0.3 (this only happen when x is greater than y, when x is 2 and y is 1, or when x is 3 and y is 1, or when x is 3 and y is 2)