se you ave no reaso Suppose a cashier gives you a dollar change. distrust this coin your prior is very high that this is a fair coin. In fact, your prior belief of the probability of the coin to give heads p(H) is the following probability distribution: p (p(H) = 0) = C 850 (1 - 0)5⁰ de where C is just a normalization constant for the distribution to sum to 1:

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Chapter1: Combinatorial Analysis
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Suppose a cashier gives you a dollar coin in change. Because you have no reason to
distrust this coin your prior is very high that this is a fair coin.
In fact, your prior belief of the probability of the coin to give heads p(H) is the
following probability distribution:
p (p(H) = 0) = C 050 (1-0)5⁰ de
where C is just a normalization constant for the distribution to sum to 1:
61/112
11/12
59/108
You decide to flip the coin 10 times, and all 10 times it turns out head. What is your
maximum a posteriori estimate (MAP) for the probability of the coin to give heads?
1
60/110
C =
0
1/2
1
S²050 (1-0) 50
Transcribed Image Text:Suppose a cashier gives you a dollar coin in change. Because you have no reason to distrust this coin your prior is very high that this is a fair coin. In fact, your prior belief of the probability of the coin to give heads p(H) is the following probability distribution: p (p(H) = 0) = C 050 (1-0)5⁰ de where C is just a normalization constant for the distribution to sum to 1: 61/112 11/12 59/108 You decide to flip the coin 10 times, and all 10 times it turns out head. What is your maximum a posteriori estimate (MAP) for the probability of the coin to give heads? 1 60/110 C = 0 1/2 1 S²050 (1-0) 50
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