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A game is played using a four-sided wooden top, with one of four letters on...

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Calculus

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A game is played using a four-sided wooden top, with one of four letters on each face, A, B, C, or D. Players compete for a pot of tokens. A player spins the top andtakes one of the following actions, depending on which letter faces up.If A faces up, the player neither adds nor subtracts tokens from the pot.If B faces up, the player wins the entire pot of tokens. If C faces up, the player wins half of the tokens in the pot, rounding up if the number is odd. If D faces up, the player adds a token to the pot.Assume that each face of the top is equally likely to face upward and that the pot holds 27 tokens. Let the random variable X be the amount of tokens won by aplayer. Thus, the range of X is {-1,0,14,27). Let the probability mass function be f(x) = P(X=x) and the cumulative probability function be F(x)=P(X ?x). Find f(0) andF(0).First, find the probability mass function f(x).f(x) ==(Type an ordered pair. Use a comma to separate answers as needed.)Now find f(0).f(0) = (Simplify your answer.)Find the cumulative probability function F(x)= P(X ?x). Choose the correct answer below.A.B.OC.0.25 -1

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