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A geometric distribution has a pdf given by P(X = x) = p(1-p)^x, where x =...

A geometric distribution has a pdf given by P(X = x) = p(1-p)^x, where x = 0, 1, 2,..., and 0 < p < 1. This form of the geometric starts at x=0, not at x=1. Given are the following properties: E(X) = (1-p)/p and Var(X) = (1-p)/p^2 A random sample of size n is drawn, the data x1, x2, ..., xn.

Likelihood is p = 1/(1+ x̄))

MLE is p̂ = 1/(1 + x̄))

asymptotic distribution is p̂ ~ N(p, (p^2-p^3/p))

Write the form of an approximate 100(1-α)% confidence interval for p.

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