Distributionshard
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Let X1,X2,,XnX_1, X_2, \dots, X_n be i.i.d. random variables with the PDF f(x)=12exf(x) = \frac{1}{2}e^{-|x|}. What is the maximum likelihood estimator for the location parameter μ\mu if the distribution is shifted to f(xμ)=12exμf(x-\mu) = \frac{1}{2}e^{-|x-\mu|}?