(Solution) - Suppose that X1 Xn form a -(2025 Original AI-Free Solution)

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Suppose that X1, . . . , Xn form a random sample from the Bernoulli distribution with unknown parameter p, and the prior p.d.f. of p is a positive and differentiable function over the interval 0 < p < 1. Suppose, furthermore, that n is large, the observed values of X1, . . . , Xn are X1, . . . , Xn, and 0 < Xn < 1. Show that the posterior distribution of p will be approximately a normal distribution with mean Xn and variance Xn(1? Xn)/n.