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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 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 28 tokens. Let the random variable X be the amount of tokens won by a player. Thus, the range of X is {-1,0,14,28}. Let the probability mass function be f(x) = P(X=x) and the cumulative probability function be F(x) = P(X

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 28 tokens. Let the random variable X be the amount of tokens won by a player. Thus, the range of X is {-1,0,14,28}. Let the probability mass function be f(x) = P(X=x) and the cumulative probability function be F(x) = P(X

A First Course in Probability (10th Edition)
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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This is one question, but I couldn't fit it all in one photo so I attached two photos. :)

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 28 tokens. Let the random variable X be the amount of tokens won by a player. Thus, the range of X is {- 1,0,14,28}. Let the probability mass function be f(x) =P(X=x) and the cumulative probability function be F(x) = P(X<x). Find f(11) and F(11).
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 28 tokens. Let the random variable X be the amount of tokens won by a player. Thus, the range of X is {- 1,0,14,28}. Let the probability mass function be f(x) =P(X=x) and the cumulative probability function be F(x) = P(X<x). Find f(11) and F(11).
Part a Now find F(11). F(11) = (Simplify your answer.) Part b 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(11). f(11) = (Simplify your answer.) %3D Find the cumulative probability function F(x)=P(X<x). Choose the correct answer below. OA. OB. OC. OD. 0.25 - 13x< 0 X< - 1 0 x< -1 x< - 1 F(X) = 0.5 Osx<14 0.25 - 1sx< 0 F(x) = < 1 - 1sxs28 0.25 - 1sx<0 F(x) = . 0.75 14sx< 28 F(x) = { 0.5 Osx<14 O 28 <x 0.75 Osx<28 0.75 14 sx< 28 1 28 sx 28 sx
Transcribed Image Text:Part a Now find F(11). F(11) = (Simplify your answer.) Part b 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(11). f(11) = (Simplify your answer.) %3D Find the cumulative probability function F(x)=P(X<x). Choose the correct answer below. OA. OB. OC. OD. 0.25 - 13x< 0 X< - 1 0 x< -1 x< - 1 F(X) = 0.5 Osx<14 0.25 - 1sx< 0 F(x) = < 1 - 1sxs28 0.25 - 1sx<0 F(x) = . 0.75 14sx< 28 F(x) = { 0.5 Osx<14 O 28 <x 0.75 Osx<28 0.75 14 sx< 28 1 28 sx 28 sx
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