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Distributionshard
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Let X1,X2,…,XnX_1, X_2, \dots, X_nX1​,X2​,…,Xn​ be i.i.d. random variables with the PDF f(x)=12e−∣x∣f(x) = \frac{1}{2}e^{-|x|}f(x)=21​e−∣x∣. What is the maximum likelihood estimator for the location parameter μ\muμ if the distribution is shifted to f(x−μ)=12e−∣x−μ∣f(x-\mu) = \frac{1}{2}e^{-|x-\mu|}f(x−μ)=21​e−∣x−μ∣?