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.