Suppose you play a game of chance in which you choose 3 balls from a boxcontaining 7 red balls, 10 black balls and 13 white balls without replacement. Ifa black ball is selected then you will get $5,

Suppose you play a game of chance in which you choose 3 balls from a boxcontaining 7 red balls, 10 black balls and 13 white balls without replacement. Ifa black ball is selected then you will get $5, if a white ball is selected then youwill get $3 and you will loose $5 for each red ball selected. Let X denote yourwining.1. Find the pmf of X.2. Find the mean and variance of X.3. Find the conditional pmf of X given B & D. {B = X <= 0},{D=First two balls picked are red}.4. Find the E[Y], where Y=2X+3.