这是一份stanford斯坦福大学 STATS205作业代写的成功案
问题 1.
\begin{aligned}
r(x) & \equiv \mathbb{E}(Y \mid X=x)=b(\theta(x)) \
\sigma^{2}(x) & \equiv \mathbb{V}(Y \mid X=x)=a(\phi) b^{\prime \prime}(\theta(x))
\end{aligned}
证明 .
The usual parametric form of this model is
$$
g(r(x))=x^{T} \beta
$$
.
STATS205 COURSE NOTES ：
For example, if $Y$ given $X=x$ is Binomial $(m, r(x))$ then
$$
f(y \mid x)=\left(\begin{array}{c}
m \
y
\end{array}\right) r(x)^{y}(1-r(x))^{m-y}
$$
which has the form (5.111) with
$$
\theta(x)=\log \frac{r(x)}{1-r(x)}, \quad b(\theta)=m \log \left(1+e^{\theta}\right)
$$