Please help me with these questions

Questions: 1. Consider a game of chance with the following rules: I It costs $1 for the player to enter the round 0 Each round, the player announces a single number in the set {1, 2, 3, 4, 5, 6} a Three fair six-sided dices are rolled o 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. Find the expected value and standard deviation of this game and determine if this is a fair game to be playing. 2. 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 f X (at) (the probability mass function of X) and plot it. (c) Now we toss a fair coin 4 times and we denote by Y the difference between the number of heads and the number of tails obtained. In this case, the probability mass function of Y is given by y -4 -2 O 2 4 \"\"- Using your knowledge about probability mass functions (i.e. without computing the dif- ferent elements in the sample space), can you tell What a should be? Justify your