6. Let X and Y be the time (in years) required to develop a superweapon for Sith and Jedi, respectively. The joint density for X and Y is given as -(aty) >0, y20 fxY(x, y) = O.W. (a) Are X and Y independent? Show your work. (b) Yoda foresees the future and finds out that none of them succeeded in developing the weapon within 253 days, which is log 2 years. Find fxyja(x, y), the conditional joint pdf of X and Y, given the event that A = {X > log 2, Y > log 2}. (log is natural log)