Suppose Xi are independent for i = 1,...,n, with common density 1 2 exp(|x |), where

Suppose Xi are independent for i = 1,...,n, with common density 1

2 exp(−|x − θ|), where θ is a parameter, x is real, and n is odd. Show that the MLE for θ is the sample median. Hint: see exercise 2B18.