Suppose you assign a Beta(a, 3) prior distribution for 0, and then you observe y heads out of n spins. It can be shown algebraically that your posterior mean of always lies between your prior mean, , and the observed relative frequency of heads, 2. This is provided as food for thought and you do not need to show it. α Show that, if the prior distribution on is uniform, the posterior variance of 0 is always less than the prior variance.

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