stat310

Homework 09

This homework follows the standard late penalty: 0% if in the stat310 mailbox by Thursday 5 Apr 4pm, 10% by 5pm the following day, 100% otherwise. Please read the syllabus for other homework policies.

  1. (6 pts) Using methods of moments,

    1. Find the estimators for Binomial(n, p).
    2. Find the estimators for Normal(\(\mu \), \( \sigma^{2} \)).
    3. For Exponential(\( \theta \)). Find two methods of moments estimators for \( \theta \).

  2. (4 pts) An estimator of \(\lambda \) when \( X_{i} \overset{iid}{\sim} \mbox{Poisson}(\lambda) \) is \( \frac{\sum X_{i}}{n} \).

    1. Is this estimator unbiased?
    2. Does it converge to \(\lambda \)? Why?

  3. (4 pts) Find the maximum likelihood estimator of \(\theta \) when X_i come from an iid exponential distribution.