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Suppose that there is a Beta(2,2) prior distribution on the probability theta that a coin will yield a "head" when spun in a specified manner.

Suppose that there is a Beta(2,2) prior distribution on the probability theta that a coin will
yield a "head" when spun in a specified manner. The coin is independently spun 10 times,
and "heads" appears 3 times.
(a) Calculate the posterior mean
(b) Calculate the posterior variance
(c) Calculate the posterior probability that 0.45 < theta<0 .55.
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