Let X1, , Xn be an i.i.d. sample from a Rayleigh distribution with parameter > 0:
a Find the method of moments estimate of .
b Find the mle of .
c Find the asymptotic variance of the mie.
The double exponential distribution is
For an i.i.d. sample of size n =2m Â± 1, show that the mie of Â 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) = Â is not differentiable. Draw a picture for a small value of n to try to understand what is going on.]