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
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Please use the Rstudio to figture out if possible, Thank you.
![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdff40a05-5e58-452b-bf5a-be8c89394b3e%2F1bc97c00-08ba-43d9-881b-5fa79fd3935a%2F2wnf7lr_processed.png&w=3840&q=75)
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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdff40a05-5e58-452b-bf5a-be8c89394b3e%2F1bc97c00-08ba-43d9-881b-5fa79fd3935a%2F7mzax92_processed.png&w=3840&q=75)
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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