in a casino, you play the following game: you choose a number between 1 and 6 and then throw 3 fair six-sided dice. after tossing, for each die showing your chosen number, the casino pays you $1. In order to play this game, you have to pay the casino a stake of S1 Let X denote your net win after one round of gambling (i.e., the payment received from the casino minus your stake) (a) Determine the state space Sx of X (b) Compute the probability mass function px of X (c) Compute the expected value E[X] of X (d) In general, a game is called a fair game if the net win of the gambler is 0 "on average" Is the above game a fair game? If not, what should be the stake of the gambler in order to make this a fair game? Give a reason for your answer.