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 30 tokens. Let the random variable X be the amount of tokens won by a player. Thus, the range of X is {-1,0,15,30). Let the probability mass function be f(x) = P(X=x) and the cumulative probability function be F(x) = P(X ≤x). Find f(9) and F(9). ... 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(9). f(9) = (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 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 30 tokens. Let the random variable X be the amount of tokens won by a player. Thus, the range of X is {-1,0,15,30). Let the probability mass function be f(x) = P(X=x) and the cumulative probability function be F(x) = P(X ≤x). Find f(9) and F(9). ... 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(9). f(9) = (Simplify your answer.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Find the cumulative probability function F(x) = P(X≤x). Choose the correct answer below.
O A.
O B.
O C.
0
x < -1
0 x < -1
F(x)=
F(x) =
0.25 -1<x<0
0.75 0<x<30
F(x)=1-1≤x≤30
0 30<x
1
30 sx
Now find F(9).
F(9)= (Simplify your answer.)
0.25 -1<x<0
0.5 0≤x≤15
0.75 15 x 30
OD.
0 x<-1
0.25 -1<x<0
F(x)= 0.5 0<x<15
0.75
15 <x<30
30 ≤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 30 tokens. Let the random variable X be the amount of tokens won by a
player. Thus, the range of X is {-1,0,15,30). Let the probability mass function be f(x) = P(X=x) and the cumulative probability function be F(x) = P(X ≤x). Find f(9)
and F(9).
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(9).
f(9) = (Simplify your answer.)
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