这是一份metrostate大都会州立大学 STAT 341作业代写的成功案
问题 1.
$$
f(u)=\exp (u) \exp {-\exp (u)}
$$
where $\mathrm{E}(U)=0.5704$ and $\operatorname{var}(U)=\pi^{2} / 6$. The cumulative distribution function has a convenient closed form
$$
F(u)=1-\exp {-\exp (u)} .
$$
证明 .
For individual-level data, we may again use the random utility function or latent variable framework
$$
y_{i}^{*}=\mathbf{x}{i}^{\prime} \beta+\varepsilon{i},
$$
STAT 341 COURSE NOTES ：
Similarly, subscript $+j$ stands for the column marginal total:
$$
f_{+j}=\sum_{i=1}^{I} f_{i j} \quad \text { and } \quad F_{+j}=\sum_{i=1}^{I} F_{i j},
$$
and subscript $++$ represents the grand total:
$$
f_{++}=\sum_{j=1}^{J} \sum_{i=1}^{I} f_{i j} \quad \text { and } \quad F_{++}=\sum_{j=1}^{J} \sum_{i=1}^{I} F_{i j} .
$$