A certain factory produces coins which are generally not fair coin. Each coin fr

Question

A certain factory produces coins which are generally not fair coin.  Each coin from the factory comes up heads with a certain probability( p) which is uniformly random on the interval [0,1].  Each coin is independent from each other coin.  (That is, the prior distribution of  (p) is uniform.)

You get a coin from this factory, fresh off the line, about which you know nothing other than that it came from the factory.  (So, at this moment in time, the expected value of (p) for this coin is .5.)  You flip the coin three times and get heads, heads, tails.

What is the Bayesian estimator for (p) for your coin? That is, what is the updated expected value of (p), taking the experiment into account?

Explanation / Answer

Bayesian estimator for (p) = 1+success /2+attempts

here success = no of heads and attempts = 3

so p = 1+2/2+3 = 3/5 = 0.6

So Bayesuan estimator p for the coin = 0.6

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