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(a) First assume that n = 5 and B = 100. Let X be the total amount that you end up paying. For each of the three versions of the game, describe the distribution of X and compute E(X) and var(X). Show your work and explain your reasoning. (b) Comment about the nature of the game in the n = 1 and n = :2 cases. (c) Bonus: Repeat part (a), but leave your answers in terms of n and B.

(a) First assume that n = 5 and B = 100. Let X be the total amount that you end up paying. For each of the three versions of the game, describe the distribution of X and compute E(X) and var(X). Show your work and explain your reasoning. (b) Comment about the nature of the game in the n = 1 and n = :2 cases. (c) Bonus: Repeat part (a), but leave your answers in terms of n and B.

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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(1) Credit Card Roulette whole number which includes yourself), and the bill arrives and is B dollars. One way to determine how to pay the bill is to play a game of chance sometimes known as "credit card rouelette": each person puts a credit card into a hat and one card is picked "uniformly at random" (each card has an equal chance of being picked). Suppose you are out to dinner with n friends (a positive Consider the following three versions of the game: • (you don't play) The bill is split evenly among all n people. Everyone gives the owner of the picked card a high-five. • (card picked "wins") The bill is split evenly among the n – 1 people whose cards were not picked. (card picked "loses") The bill is paid entirely by the one person whose card was picked. 5 and B 100. Let X be the total amount that you end (a) First assume that n = up paying. For each of the three versions of the game, describe the distribution of X and compute E(X) and var(X). Show your work and explain your reasoning. (b) Comment about the nature of the game in the n = 1 and n 2 cases. (c) Bonus: Repeat part (a), but leave your answers in terms of n and B.
Transcribed Image Text:(1) Credit Card Roulette whole number which includes yourself), and the bill arrives and is B dollars. One way to determine how to pay the bill is to play a game of chance sometimes known as "credit card rouelette": each person puts a credit card into a hat and one card is picked "uniformly at random" (each card has an equal chance of being picked). Suppose you are out to dinner with n friends (a positive Consider the following three versions of the game: • (you don't play) The bill is split evenly among all n people. Everyone gives the owner of the picked card a high-five. • (card picked "wins") The bill is split evenly among the n – 1 people whose cards were not picked. (card picked "loses") The bill is paid entirely by the one person whose card was picked. 5 and B 100. Let X be the total amount that you end (a) First assume that n = up paying. For each of the three versions of the game, describe the distribution of X and compute E(X) and var(X). Show your work and explain your reasoning. (b) Comment about the nature of the game in the n = 1 and n 2 cases. (c) Bonus: Repeat part (a), but leave your answers in terms of n and B.
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