Question: Problem 4. (18 points) Assume a sample X1, X2 ... X, are i.i.d. random variables from a distribution given below. (a) Assume that the sample

Problem 4. (18 points) Assume a sample X1, X2 ... X,

Problem 4. (18 points) Assume a sample X1, X2 ... X, are i.i.d. random variables from a distribution given below. (a) Assume that the sample is from a distribution with density function f(| () = = exp IT . Note that here |denotes the absolute value of x. Please find the maximum likelihood estimate of o. (b) Assume that the sample is from the Pareto distribution, which has been used in economics as a model for a density function with a slowly decaying tail. The density function is given by f(x | ro, 0) = Orgx- - 0-1 , x 2 0 0>1. Here To >0 is given. Please find the maximum likelihood estimate of 0

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