The double exponential distribution is For an i.i.d. sample of size n = 2m + 1,...

The double exponential distribution is

For an i.i.d. sample of size n = 2m + 1, show that the mle of θ is the median of the sample. (The observation such that half of the rest of the observations are smaller and half are larger.) [Hint: The function g(x) = |x| is not differentiable. Draw a picture for a small value of n to try to understand what is going on.]