The differentiation approach to derive the maximum likelihood estimator (mle) is not appropriate in all the cases. Let X₁, X2, X, be a random sample of size n from the population of X. Consider the probability function of X -{. [e-(2-0), if 0≤x<∞ for -∞ <<∞ otherwise. f(x;0)= (a) Argue that the mle of is the first order statistic (Y₁). Denote it by . (b) Find E(), and show that the mle of 0 is a biased estimator. (c) Derive the mean square error (mse) of 6.

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