Homework 14

Problems

Section 6.2:

13, 15, 17, 19

Section 7.1:

1, 2, 3, 10

Additional Problem

Let $X \sim \text{Binomial}(n, \theta)$, and consider the estimator $\bar{\theta}_{n} = \dfrac{X + 1}{n + 2}$ for the success probability $\theta$.

a. Determine the expected value of $\bar{\theta}_{n}$. What is the expected value of $\bar{\theta}_{n}$ as $n \to \infty$?

b. Determine the variance of $\bar{\theta}_{n}$.

c. Determine the standard error of $\bar{\theta}_{n}$.

d. How does the estimator $\bar{\theta}_{n}$ compare the estimator $\widehat{\theta}_{n} = X /n$ we discussed in class?