Please help me with this question

1. Consider a game of chance with the following rules:

It costs $1 for the player to enter the round

Each round, the player announces a single number in the set

{1, 2, 3, 4, 5, 6}

Three fair six-sided dices are rolled

For each die that shows the number announced, the player wins $1.

For example, the player pays $ 1 to enter the game and announces the number 2. If the outcome of the roll is 3, 2, 2 then the player gets back $2. However, if the outcome is 4,5,6 then the player gets nothing back.

We toss a fair coin 3 times. We denote by X the difference between the number of heads and the number of tails obtained (that is X= #H#T).

(a) Calculate fx(X) (the probability mass function of X) and plot it.

(b) Calculate E(X) and Var(X).