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Q1. Let p denote the probability that the coin will turn up as a Head when...

Q1. Let p denote the probability that the coin will turn up as a Head when tossed. Given n independent tosses of the same coin, what is the probability distribution associated with the number of Head outcomes observed?

Q2. Suppose you have information that a coin in your possession is not a fair coin, and further that either Pr(Head|p) = p is certain to be equal to either p = 0.33 or p = 0.66. Assuming you believe this information, but are otherwise uncertain about which of the two values is the correct probability, detail the corresponding prior probabilities associated with the possible values of p.

Q3. You set about trying to determine the correct value of p by independently tossing the coin n times, and you observe exactly x outcomes. Using your prior distribution from Q2, detail the form of the resulting posterior distribution and explain how it is derived.

Q4. Compute the relevant posterior probabilities in each of the following cases corresponding to the setting in Q3: a. You toss the coin only one time, and get a Head outcome. b. You independently toss the coin 25 times, and get 11 Head outcomes (“Heads”). c. You independently toss the coin 100 times, and get 48 Heads.

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