Two random variables have a joint probability distribution function defined by F(x, y) = 0 x < 0, y < 0 0 ly > 1 = xy = 1 ) Sketch this distribution function. ) Find the joint probability density function and sketch it. ) Find the joint probability of the event X < | and Y > !.

Let f(x) = x for 0 < x < 1. Is f(x) a legitimate probability distribution function (pdf) for a continuous random variable?     No, the area under f(x) is not 1 (it is greater than 1).     Yes, all criteria for a pdf are satisfied.     No, the area under f(x) is not 1 (it it less than 1).     No, f(x) is not non-negative.

If the joint probability distribution of X and Yis given by: (picture)Find P(X ≤ 2, Y = 1)Find P(X + Y = 4)Find P(X>Y )Find P(X > 2, Y ≤ 1)