Originally Posted by
James1220 A random sample of two functions x1, x2, is drawn from the distribution with pdf:
2/θ^2 (θ - x) 0<x<θ
f(x;θ) = {
0 otherwise
find the method of moments estimator of θ and show that it is not bias.
With help of fellow mathematicians, i found the solution to the above problem. the following question relates to this and is the second part of the question :
Show that the maximum likelihood estimator of θ is given by:
\hat{\theta} = 1/4 [3(x_1 + x_2) + Square root of (9x_1^2 - 14x_1x_2 + 9x_2^2)]
Im troubled because of the fact that there are 2 variables x_1 and x_2, so i'm having trouble finding how to fond the mle. Help if you can Pleaseee!