Suppose that X1, X2, . . . , Xn are i.i.d. random
Chapter , Problem 17(choose chapter or problem)
Suppose that \(X_{1}, X_{2}, \ldots, X_{n}\) are i.i.d. random variables on the interval [0, 1] with the density function
\(f(x \mid \alpha)=\frac{\Gamma(2 \alpha)}{\Gamma(\alpha)^{2}}[x(1-x)]^{\alpha-1}\)
where \(\alpha>0\) is a parameter to be estimated from the sample. It can be shown that
\(\begin{aligned}E(X) & =\frac{1}{2} \\ \operatorname{Var}(X) & =\frac{1}{4(2 \alpha+1)}\end{aligned}\)
a. How does the shape of the density depend on \(\alpha\)?
b. How can the method of moments be used to estimate \(\alpha\)?
c. What equation does the mle of \(\alpha\) satisfy?
d. What is the asymptotic variance of the mle?
e. Find a sufficient statistic for \(\alpha\).
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer