Question: (Bayesian estimation) Assume you have a biased coin with a Uniform[0, 1] prior for p, the probability that the coin lands on heads. You toss

(Bayesian estimation) Assume you have a biased coin with a Uniform[0, 1] prior for p, the probability that the coin lands on heads. You toss the coin 5 times successively. You obtain H, H, H, T, H. Suppose you apply Bayes rule to update your belief after each observation. How do the mean, mode, and variance of your belief about p evolve as you make these 5 successive observations? (Give values for the mean, mode, and variance of your belief about p after each coin flip). After observing these five outcomes, what is the probability the coin is biased towards heads (that is, the probability of observing heads is larger than 0.5)? Can you make a similar statement from the frequentist perspective?

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