Question 1 1 pts You pay us $6 to participate in a game. As a function of the roll of a die, we will then pay you some amount of money which we will call a "payoff". Let X denote the amount won by playing the game as a function of the roll of the die (including the initial $6 you had to expense to participate in the game): Number on the dice Payoff X 0 3 -3 4 -2 4 5 -1 6 0 6 12 6 Assume that the dice is fair, which means the probability of observing any number is equally 1/6. Which of the following is true? O Vart-3X + 5) - 120 If both the amount you pay to play the game and the payoff's were doubled, thereby doubling the value of X for each roll of the die, the expected gain would be a loss of 1.5 dollars. 0 EDX)= =0.147 O The standard deviation of X is 13.33