Shankar really likes playing Badminton. On a particular day at Fetzer gym he plays two games (whose outcomes are independent of each other). He has .3 probability of winning the first game and he has .9 probability of winning the second game. There are no ties and as stated above the outcomes of each game are independent of each other. Let X denote the number of games Shankar wins.
a. Calculate E[X] and E[X2].
b. Find a formula for M(t), the moment generating function for X.
c. Find a formula for M'(t) and check that M'(0) = E[X].
d. Find a forumla for M"(t) and use it to find Var[X].