---
title: "Biostat 200C Homework 3"
subtitle: Due May 8 @ 11:59PM
output: 
  html_document:
    toc: true
    toc_depth: 4
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, cache = FALSE)
```

## Q1. Moments of exponential family distributions

Show that the exponential family distributions have moments
\begin{eqnarray*}
  \mathbb{E}Y &=& \mu = b'(\theta) \\
  \operatorname{Var}Y &=& \sigma^2 = b''(\theta) a(\phi).
\end{eqnarray*}

## Q2. Score and information matrix of GLM

Derive the gradient (score), negative Hessian, and Fisher information matrix (expected negative Hessian) of GLM.

## Q3. ELMR Exercise 8.1 (p171)

## Q4. ELMR Exercise 8.4 (p172)

## Q5. ELMR Exercise 8.5 (p172)