The double exponential distribution is f (x
Chapter , Problem 51(choose chapter or problem)
The double exponential distribution is
\(f(x \mid \theta)=\frac{1}{2} e^{-|x-\theta|}, \quad-\infty<x<\infty\)
For an i.i.d. sample of size n = 2m + 1, show that the mle of \(\theta\) 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.]
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