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Homework 1 Solutions
1.1 Closed Form Estimation 1.(3pts) An exponential distribution with parameter follows a distribution p(x) = e x. Given some i.i.d. data fx ign i=1 ˘Exp( ), derive the maximum likelihood estimate (MLE) ^ MLE. Is this estimator biased? Solution: The log likelihood is l( ) = X i log x i= nlog X i x i Set the derivative to 0: n= X i x i= 0 ) = 1 ...
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