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3. At a carnival, there is a single player game called the High Striker. Here is how the game works: • A player takes a mallet and swings it at a target that is located at the base of the High Striker. • For every swing that a player takes, they receive a score that is directly proportional to the force of that swing. If the player's score on any given swing is greater than y (where y> 0), then the player wins a prize. A player may swing as many times as they like during the game. There is no limit on the number of prizes that a player can win during the game. Players are classified as either fit with probability p or unfit with probability 1- p. Players are also classified as either competitive or non-competitive. A fit player has probability c, of being competitive, whereas an unfit player has probability cu of being competitive. On any given swing, the score received by a fit player follows a U(0, m) distribution, whereas the score received by an unfit player follows a U(0, m/2) distribution where y

3. At a carnival, there is a single player game called the High Striker. Here is how the game works: • A player takes a mallet and swings it at a target that is located at the base of the High Striker. • For every swing that a player takes, they receive a score that is directly proportional to the force of that swing. If the player's score on any given swing is greater than y (where y> 0), then the player wins a prize. A player may swing as many times as they like during the game. There is no limit on the number of prizes that a player can win during the game. Players are classified as either fit with probability p or unfit with probability 1- p. Players are also classified as either competitive or non-competitive. A fit player has probability c, of being competitive, whereas an unfit player has probability cu of being competitive. On any given swing, the score received by a fit player follows a U(0, m) distribution, whereas the score received by an unfit player follows a U(0, m/2) distribution where y

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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3. At a carnival, there is a single player game called the High Striker. Here is how the game works: • A player takes a mallet and swings it at a target that is located at the base of the High Striker. • For every swing that a player takes, they receive a score that is directly proportional to the force of that swing. • If the player's score on any given swing is greater than y (where y > 0), then the player wins a prize. • A player may swing as many times as they like during the game. • There is no limit on the number of prizes that a player can win during the game. Players are classified as either fit with probability p or unfit with probability 1 – p. Players are also classified as either competitive or non-competitive. A fit player has probability cf of being competitive, whereas an unfit player has probability cu of being competitive. On any given swing, the score received by a fit player follows a U(0, m) distribution, whereas the score received by an unfit player follows a U(0, m/2) distribution where y < m/2. Assume that the scores received on each swing are mutually independent. Non-competitive players will continue to swing at the target until they win one prize, after which they will quit the game. Competitive players will continue to swing at the target until they win L prizes, after which they will quit the game. We assume that L is a rv having a POI(X) distribution that is shifted 1 unit to the right and is independent of all else in this question. A player's max score refers to the highest score they receive while playing the game. (a) Determine the expected number of swings taken by a randomly chosen player while playing the game. (b) Given a player is fit and competitive, determine the probability that their max score is less than or equal to z where y < z< m.
Transcribed Image Text:3. At a carnival, there is a single player game called the High Striker. Here is how the game works: • A player takes a mallet and swings it at a target that is located at the base of the High Striker. • For every swing that a player takes, they receive a score that is directly proportional to the force of that swing. • If the player's score on any given swing is greater than y (where y > 0), then the player wins a prize. • A player may swing as many times as they like during the game. • There is no limit on the number of prizes that a player can win during the game. Players are classified as either fit with probability p or unfit with probability 1 – p. Players are also classified as either competitive or non-competitive. A fit player has probability cf of being competitive, whereas an unfit player has probability cu of being competitive. On any given swing, the score received by a fit player follows a U(0, m) distribution, whereas the score received by an unfit player follows a U(0, m/2) distribution where y < m/2. Assume that the scores received on each swing are mutually independent. Non-competitive players will continue to swing at the target until they win one prize, after which they will quit the game. Competitive players will continue to swing at the target until they win L prizes, after which they will quit the game. We assume that L is a rv having a POI(X) distribution that is shifted 1 unit to the right and is independent of all else in this question. A player's max score refers to the highest score they receive while playing the game. (a) Determine the expected number of swings taken by a randomly chosen player while playing the game. (b) Given a player is fit and competitive, determine the probability that their max score is less than or equal to z where y < z< m.
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