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A particular coin is biased. Each time it is flipped, the probability of getting a head is P(H) = 0.7 . Each flip is independent of the other flips. a) In a game, the coin is flipped 10 times. Let X be the total number of times the coin shows a head out of 10 flips. Calculate the following probabilities: i) What is the probability of getting exactly 4 heads?

A particular coin is biased. Each time it is flipped, the probability of getting a head is P(H) = 0.7 . Each flip is independent of the other flips. a) In a game, the coin is flipped 10 times. Let X be the total number of times the coin shows a head out of 10 flips. Calculate the following probabilities: i) What is the probability of getting exactly 4 heads?

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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A particular coin is biased. Each time it is flipped, the probability of getting a head is P(H) = 0.7 . Each flip is independent of the other flips. a) In a game, the coin is flipped 10 times. Let X be the total number of times the coin shows a head out of 10 flips. Calculate the following probabilities: i) What is the probability of getting exactly 4 heads? ii) What is the probability of getting at most 4 heads? iii) What is the probability of getting more than 4 heads? i) Compute the expected value. "x= (Enter your answer correct to at least 3 decimal places) ii) Compute the variance. b) We now want to compute the expected value and variance of X. 34 (Enter your answer correct to at least 3 decimal places) = (Enter your answer correct to at least 3 decimal places) (Enter the exact value) (Enter the exact value) c) When you play the game, you need to pay 8 dollars to enter the game, then you toss the coin 10 times. You win 4 dollars per head. Let Y be the net amount you win when you play this game (once).
Transcribed Image Text:A particular coin is biased. Each time it is flipped, the probability of getting a head is P(H) = 0.7 . Each flip is independent of the other flips. a) In a game, the coin is flipped 10 times. Let X be the total number of times the coin shows a head out of 10 flips. Calculate the following probabilities: i) What is the probability of getting exactly 4 heads? ii) What is the probability of getting at most 4 heads? iii) What is the probability of getting more than 4 heads? i) Compute the expected value. "x= (Enter your answer correct to at least 3 decimal places) ii) Compute the variance. b) We now want to compute the expected value and variance of X. 34 (Enter your answer correct to at least 3 decimal places) = (Enter your answer correct to at least 3 decimal places) (Enter the exact value) (Enter the exact value) c) When you play the game, you need to pay 8 dollars to enter the game, then you toss the coin 10 times. You win 4 dollars per head. Let Y be the net amount you win when you play this game (once).
c) When you play the game, you need to pay 8 dollars to enter the game, then you toss the coin 10 times. You win 4 dollars per head. Let Y be the net amount you win when you play this game (once). i) How much money can you expect to win per game (net amount) if you play that game a very large number of times? $ (Enter the exact value in dollars) ii) In order to assess how risky the game is, calculate the variance of Y. (Enter the exact value)
Transcribed Image Text:c) When you play the game, you need to pay 8 dollars to enter the game, then you toss the coin 10 times. You win 4 dollars per head. Let Y be the net amount you win when you play this game (once). i) How much money can you expect to win per game (net amount) if you play that game a very large number of times? $ (Enter the exact value in dollars) ii) In order to assess how risky the game is, calculate the variance of Y. (Enter the exact value)
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