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 an- Cakes 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 26 tokens. Let the random variable X be the amount of tokens won by a layer. Thus, the range of X is {-1,0,13,26). Let the probability mass function be f(x) = P(X=x) and the cumulative probability function be F(x)=P(X ≤x). Find f(1) nd F(1). irst, find the probability mass function f(x). ype an ordered pair. Use a comma to separate answers as needed.) Ow find f(1). () = (Simplify your answer.)
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 an- Cakes 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 26 tokens. Let the random variable X be the amount of tokens won by a layer. Thus, the range of X is {-1,0,13,26). Let the probability mass function be f(x) = P(X=x) and the cumulative probability function be F(x)=P(X ≤x). Find f(1) nd F(1). irst, find the probability mass function f(x). ype an ordered pair. Use a comma to separate answers as needed.) Ow find f(1). () = (Simplify your answer.)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.CT: Chapter Test
Problem 1CT: Alice and Bill have four grandchildren, and they have three framed pictures of each grandchild. They...
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Transcribed Image Text:Find the cumulative probability function F(x) = P(X≤x). Choose the correct answer below.
OA.
O B.
O C.
0 x < -1
0
x < -1
F(x) = 1 -1sx≤26
0.25 -1<x<0
F(x) =
0 26 <x
F(x)= 0.5 0<x< 13
0.75 13 ≤x<26
26 ≤x
Now find F(1).
F(1) = (Simplify your answer.)
0.25 -1<x<0
0.5 0<x< 13
0.75 13 <x<26
OD.
F(x) =
0
x < -1
0.25 -1<x<0
0.75 0<x<26
1
26 ≤x
Transcribed Image Text: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 26 tokens. Let the random variable X be the amount of tokens won by a
player. Thus, the range of X is {-1,0,13,26). Let the probability mass function be f(x) = P(X=x) and the cumulative probability function be F(x)=P(X≤x). Find f(1)
and F(1).
First, find the probability mass function f(x).
f(x) = 0
(Type an ordered pair. Use a comma to separate answers as needed.)
Now find f(1).
f(1) = (Simplify your answer.)
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