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

Question

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 and takes 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 39 tokens. Let the random variable X be the amount of tokens won by a player. Thus, the range of X is-1,0,20,39). Let the probability mass function be f(x) = P(X=x) and the cumulative probability function be F(x)= P(Xsx) Find f(26) and F(26). 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(26). f(26)(Simplify your answer.) Find the cumulative probability function F(x)-P(Xx). Choose the correct answer below OA. O D. 0.25 -1sx

Explanation / Answer

from here f(x) =[1/4 ,1/4 ,1/4 ,1/4}

f(26)=0 (as there is no event where 26 token won by player)

for cumulative distribution: option A is correct

F(26)=f(-1)+f(0)+f(20)=1/4+1/4+1/4 =3/4

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