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Exercise 4 Suppose a factory manufacture three types of coins, with probability showing up Heads to be 0.3, 0.5, and 0.9, respectively. We are given one of these coins and do not know which type it is, and our initial belief is that the three types are equally likely. We toss the coin 10 times and get 3 Heads. Using Bayesian inference, what probabilities should we assign to the three types after this observation?

Exercise 4 Suppose a factory manufacture three types of coins, with probability showing up Heads to be 0.3, 0.5, and 0.9, respectively. We are given one of these coins and do not know which type it is, and our initial belief is that the three types are equally likely. We toss the coin 10 times and get 3 Heads. Using Bayesian inference, what probabilities should we assign to the three types after this observation?

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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Exercise 4 Suppose a factory manufacture three types of coins, with probability showing up Heads to be 0.3, 0.5, and 0.9, respectively. We are given one of these coins and do not know which type it is, and our initial belief is that the three types are equally likely. We toss the coin 10 times and get 3 Heads. Using Bayesian inference, what probabilities should we assign to the three types after this observation?
Transcribed Image Text:Exercise 4 Suppose a factory manufacture three types of coins, with probability showing up Heads to be 0.3, 0.5, and 0.9, respectively. We are given one of these coins and do not know which type it is, and our initial belief is that the three types are equally likely. We toss the coin 10 times and get 3 Heads. Using Bayesian inference, what probabilities should we assign to the three types after this observation?
Expert Solution
Step 1

Given:

Let A1,A2, and A3 be the hypothesis that a coin is of type 1, type 2, and type 3 respectively.

Thus, the prior probabilities of getting a type of coin are given below:

 P(A1)=1/3P(A2)=1/3P(A3)=1/3

Let H be the event of getting a Head in the throw when we select a coin.

Thus, the probability of getting a head type of coin is given below:

P(H  A1)=0.3P(H  A2)=0.5P(H  A3)=0.9

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