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Suppose you toss a coin and put a Uniform[0,4, 0,6] prior on A, the probability of getting a head…

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Suppose you toss a coin and put a Uniform[0,4, 0,6] prior on A, the probability of getting a head on a single toss.

If you toss the coin n times and obtain n heads, then determine the posterior density of θ

(b) Suppose the true value of θ is, in fact, 099. Will the posterior distribution of A ever put any probability mass around θ =099 for any sample of n?

 (c) What do you conclude from part (b) about how you should choose a prior ?