2 Maximum Likelihood Suppose we have n i.i.d (independent and identically distributed) data samples from the following probability distribution. This problem asks you to build a log-likelihood function, and find the maximum likelihood estimator of the parameter(s). (a) Exponential distribution The exponential distribution is defined as 1 P(x|3) - Ze #, with 0 <<∞ Please find the MLE of the parameter 3 (b) Pareto distribution[s] The Pareto distribution has been used in economics for a density function with a slowly decaying tail: f(xxo,0) = 0xox-0-1, * ≥ ro, 0>1 assume that o> 0 is given. Find the MLE of 0.

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