Let’s assume there is 1 fake coin out of 1000 coins. ( P[Coin=fake] = 0.001 )...

Let’s assume there is 1 fake coin out of 1000 coins. ( P[Coin=fake] = 0.001 ) The probability of showing head for fake coin is 0.9 (P[Head | Coin=fake] = 0.9). For normal coin, the probability of showing head is 0.5 (P[Head | Coin=normal] = 0.5).

i. Bayes theorem, If you have a coin, and toss it one time. You got a head. What is the probability that this coin is fake?

ii. If you toss a coin 10 times, you got 8 head out of ten tosses. What is the probability of this event if the coin is fair (P[X=8|Coin=normal], X is a random variable representing number of head out of ten tosses)? What is the probability of this event if the coin is fake( P[X=8|Coin=fake])?

iii. If you toss a coin 10 times, you got 8 head out of ten tosses. What is the probability that this coin is fake?

iv. Calculate the probability that you will get a head after you get 8 head out of ten tosses? What is the probability if you are Frequentist? What is it if you are Bayesian?

Expert Solution

orchestra answered 1 year ago

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