In a casino, you play the following game: You choose a number between 1 and 6...

 

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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 $1. 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. 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 $1. 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.

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Lets address each part of this question step by step a The state space SX of X Since the game involves choosing a number between 1 and 6 and then roll... View the full answer