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Suppose there are two types of coins, heads-biased coins and tails-biased coins. A heads-biased oin has a 3/4 probability of a heads, while a tails-biased coin has a 1/4 probability of heads. The roportion of all coins that are heads-biased is 1/7. Suppose that we flip a coin twice and it comes up HH. (a) For a standard Bayesian information processor: (i) What is the person's posterior probability that the coin is heads-biased? (ii) What is the person's forecast for a third flip being H?

Suppose there are two types of coins, heads-biased coins and tails-biased coins. A heads-biased oin has a 3/4 probability of a heads, while a tails-biased coin has a 1/4 probability of heads. The roportion of all coins that are heads-biased is 1/7. Suppose that we flip a coin twice and it comes up HH. (a) For a standard Bayesian information processor: (i) What is the person's posterior probability that the coin is heads-biased? (ii) What is the person's forecast for a third flip being H?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Suppose there are two types of coins, heads-biased coins and tails-biased coins. A heads-biased coin has a 3/4 probability of a heads, while a tails-biased coin has a 1/4 probability of heads. The proportion of all coins that are heads-biased is 1/7. Suppose that we flip a coin twice and it comes up HH. (a) For a standard Bayesian information processor: (i) What is the person's posterior probability that the coin is heads-biased? (ii) What is the person's forecast for a third flip being H? (b) For an (N = 8)-Freddy (as defined in class): (i) What is the person's posterior probability that the coin is heads-biased? (ii) What is the person's forecast for a third flip being H?
Transcribed Image Text:Suppose there are two types of coins, heads-biased coins and tails-biased coins. A heads-biased coin has a 3/4 probability of a heads, while a tails-biased coin has a 1/4 probability of heads. The proportion of all coins that are heads-biased is 1/7. Suppose that we flip a coin twice and it comes up HH. (a) For a standard Bayesian information processor: (i) What is the person's posterior probability that the coin is heads-biased? (ii) What is the person's forecast for a third flip being H? (b) For an (N = 8)-Freddy (as defined in class): (i) What is the person's posterior probability that the coin is heads-biased? (ii) What is the person's forecast for a third flip being H?
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