Show transcribed image text Problem 3 (45 points The join pdf of random variables X and Y is given as finlx,y)-1 for Osxs1 and Osysl, fxlx,y)-0 for else. a) (10 pts) Find marginal pdf fu(x) for X, fly) for Y, and plot fulx) and fuly) b) (5 pts) Are X and Y independent? Why? c) (15 pts) Find the mean of X, the mean of Y, E[XY] d) (15 pts) Find the probability of event (YsX,) 0 CXO
Problem 3 (45 points The join pdf of random variables X and Y is given as finlx,y)-1 for Osxs1 and Osysl, fxlx,y)-0 for else. a) (10 pts) Find marginal pdf fu(x) for X, fly) for Y, and plot fulx) and fuly) b) (5 pts) Are X and Y independent? Why? c) (15 pts) Find the mean of X, the mean of Y, E[XY] d) (15 pts) Find the probability of event (YsX,) 0 CXO
