Gasoline is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. The joint density of Y1, the proportion of the capacity of the tank that is stocked at the beginning of the week, and Y2, the proportion of the capacity sold during the week, is given by 3y 0 S y s y s 1 f I = 1r 2 1 . (yl yz) l0, elsewhere. (a) Find the marginal density function for Y2. W2) = where: S V2 S :l (b) For what values of 1/2 is the conditional density f(y1|y2) defined? Swim/:15: (c) What is the probability that more than half a tank is sold given that two-thirds of a tank is stocked? (Enter your probability as a fraction.) :l