Problem 4: Suppose you play a game 5 times and each time you have a probability
(1)/(3)
of winning. The game costs
$1
to play each time. Each time you win, you earn
$10
. (a) Let
x
be the number of games you win. What kind of random variable is this? Write the probability mass function for
x
. (b) Let
Y
be the net amount of money you are left with at the end of all five games. Write a probability mass function for
Y
.