In the board game, a player in jail gets out by rolling "doubles" on their turn, i.e., by rolling the same number on the two dice thrown. Let X be the outcome of a single roll of the two dice, with "success" considered to be rolling doubles and "failure" rolling anything else.

(a) Name the distribution of X, and give the name(s) and value(s) of the parameter(s)

(b) Now, suppose we roll two dice 3 times. Define Y to be the number of times doubles are rolled in the 3 trials. Name the distribution of Y, and give the name(s) and value(s) of the parameter(s)

(c) Find the expected value and variance of Y

(d) After the 3rd failed attempt to roll doubles, a player must pay the $50 fine and leave jail. What is the expected payment($) to get out of jail?