(a) Find the maximum- likelihood estimator for u, the population mean, given a sample of size n from a population with f(x) = 1/B, 0<x<B. Estimate B by the method of moments.
(b)The sample 1.3,0.6,1.7,2.2,0.3,1.1 was drawn from a population with the density f(x) = 1/B, 0<x<B. What are the maximum-likelihood estimates of the mean and variance of the population?
so far i know that
f(x) = (1/B) ^n
ln f(x) = n (1/B)
d ln f(x)/ dB = -n/B^2
any suggestions on where i went wrong?
you can't differentiate this. You need to include the indicator function, that the max is less than B.
Originally Posted by maurisa
Since the likelihood function is the max occurs when B is as small as possible
which happens when B is the largest order statistic. Since the MLE of B is the largest order stat and the mean is B/2
I guess the estimate you want is the max over 2.