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The Laplace distribution has a pdf f ( x ; , b ) = 2 b 1 exp ( b x ) . Let X

The Laplace distribution has a pdff(x;,b)=2b1exp(bx).

LetX1,...,X5iidLaplace(,1).

1) Find the method of moments estimator for .

2) Show that the maximum likelihood estimator of is the sample median.

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