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.
Please help!
Calculate E(X) as a function of $\displaystyle \theta$ using the given pdf.
Note that the sample mean is $\displaystyle \bar{X} = \frac{x_1 + x_2}{2}$. Estimate $\displaystyle \theta$ by equating E(X) to the sample mean. I get $\displaystyle \hat{\theta} = \frac{3(x_1 + x_2)}{2} = 3 \bar{X}$.
Now show that $\displaystyle E(\hat{\theta}) = \theta$.
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!
Read this thread carefully: http://www.mathhelpforum.com/math-he...estimator.html
Now try the question again.
Post if you're still stuck (please be sure to say where you're stuck).