Homework 4

Homework 4 is due 10/14/2022 at 11:59 PM. Submit your homework on Canvas as one PDF document.

The PDF version of this assignment can be found here.

1. Let X_1, X_2, \ldots, X_n be iid with the following density function

   f(x) = \left\{\begin{array}{cc} \frac{\alpha x^{\alpha-1}}{3^\alpha}& 0\le x\le 3 \\ 0 & \mathrm{elsewhere} \end{array} \right.

   Find the method of moment estimator for \alpha.

2. Let X_1, X_2, \ldots, X_n be iid with the following density function

   f(x) = \left\{\begin{array}{cc} \frac{1}{\theta}2xe^{-x^2/\theta} & 0<x;0< \theta \\ 0 & \mathrm{elsewhere} \end{array} \right.

   Find the MLE for \theta.

3. Is the MLE estimator from Problem 2 unbiased?