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1. Suppose we have Xl,. . , . xn P(x; 0) = (1 - oy-lo, x = where O < < 1. Note: E(X)

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1. Suppose we have Xl,. . , . xn P(x; 0) = (1 - oy-lo, x = where O < < 1. Note: E(X) = and Var(X) = (a) Find omle the MLE of O. (b) Find the 1(0). (c) Find the asymptotic distribution of 9mle. That is, find the part (1) and (2) of the following: Vfi(mle- (1) ) N(0, (2) ). (d) Find an asymptotic 95% confidence interval for O. Hint: the 0.95 quantile of the standard normal (Z distribution) is 1.645, and 0.975 quantile of the standard normal is 1.96.

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