Let X be distributed double exponential with density f (x) 1 2 exp(jx j) for x 2 R. (a) Find the log-likelihood function `n().

Let X be distributed double exponential with density f (x) Æ 1 2 exp(¡jx ¡µj) for x 2 R.

(a) Find the log-likelihood function `n(µ).

(b) Extra challenge: Find the MLE bµ for µ. This is challenging as it is not simply solving the FOC due to the nondifferentiability of the density function.