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Please provide clear, detailed, and neat solutions step by step for the entire problem (a-d)? Thanks! Let X1,. ...Xn be a random sample of size

Please provide clear, detailed, and neat solutions step by step for the entire problem (a-d)? Thanks!

Let X1,. ...Xn be a random sample of size n from a geometric distribution that has pm (; 0) = (1 -0)"-10, x = 1,2, .... (a) Find the MLE on of 0 and the Fisher information of the data. (b) Use asymptotic normality of the MLE to approximate the distribution of On (c) Find the Wald-type confidence interval for 0. (d) Show that EX; is a sufficient statistic for 0 and find the MVUE for 0

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