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a) Suppose you have three coins in a bag: the first coin is fair, wit! ility of HEAD (H) equals to that of TAIL (T), i.e., P(X = H\M1) = P(X = T|M1). is a binary random variable representing HEAD or TAIL. The second is a loaded co (X = H|M2) = 0.8. The third is also a loaded coin with P(X = H\M3) = 0.2. Your kes a coin out of the bag at random and flips it. When it lands, you observe that the e coin facing up is HEAD. What is the probabilities that this is the first, second an in? Hint: You may assume the three coins are equal likely to be selected from the ba M1) = P(M2) = P(M3) = }, and you need to calculate P(M1|X = H), P(M2|X = MalX = H)

a) Suppose you have three coins in a bag: the first coin is fair, wit! ility of HEAD (H) equals to that of TAIL (T), i.e., P(X = H\M1) = P(X = T|M1). is a binary random variable representing HEAD or TAIL. The second is a loaded co (X = H|M2) = 0.8. The third is also a loaded coin with P(X = H\M3) = 0.2. Your kes a coin out of the bag at random and flips it. When it lands, you observe that the e coin facing up is HEAD. What is the probabilities that this is the first, second an in? Hint: You may assume the three coins are equal likely to be selected from the ba M1) = P(M2) = P(M3) = }, and you need to calculate P(M1|X = H), P(M2|X = MalX = H)

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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5. a) Suppose you have three coins in a bag: the first coin is fair, with prob- ability of HEAD (H) equals to that of TAIL (T), i.e., P(X = H|M1) = P(X = T|M1), where X is a binary random variable representing HEAD or TAIL. The second is a loaded coin with P(X = takes a coin out of the bag at random and flips it. When it lands, you observe that the side of the coin facing up is HEAD. What is the probabilities that this is the first, second and third coin? Hint: You may assume the three coins are equal likely to be selected from the bag, i.e., P(M1) = P(M2) = P(M3) = , and you need to calculate P(M||X = H), P(M2|X = H) and P(M3|X = H). H|M2) = 0.8. The third is also a loaded coin with P(X = Н Мз) — 0.2. Your friend 6) What if we don't know the probabilities of HEAD for each coin? Design an iterative algorithm using pseudo-code to estimate these probabilities.
Transcribed Image Text:5. a) Suppose you have three coins in a bag: the first coin is fair, with prob- ability of HEAD (H) equals to that of TAIL (T), i.e., P(X = H|M1) = P(X = T|M1), where X is a binary random variable representing HEAD or TAIL. The second is a loaded coin with P(X = takes a coin out of the bag at random and flips it. When it lands, you observe that the side of the coin facing up is HEAD. What is the probabilities that this is the first, second and third coin? Hint: You may assume the three coins are equal likely to be selected from the bag, i.e., P(M1) = P(M2) = P(M3) = , and you need to calculate P(M||X = H), P(M2|X = H) and P(M3|X = H). H|M2) = 0.8. The third is also a loaded coin with P(X = Н Мз) — 0.2. Your friend 6) What if we don't know the probabilities of HEAD for each coin? Design an iterative algorithm using pseudo-code to estimate these probabilities.
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