10楼: Originally posted by hubeizk at 2014-02-24 16:29:34
\{Y_N\in A\}\cap \{N=n\}= \{N=n\}\cap \{Y_n\in A\}?还是没有看懂Y_N代表什么..........

11楼: Originally posted by jabile at 2014-02-24 16:51:40
Y_N是随机变量啊，相当于复合函数,Y_N(\omega)=Y_{N(\omega}}(\omega)...

12楼: Originally posted by hubeizk at 2014-02-25 10:07:40
可是\mathcal{F}_N按照定义不是一个事件域么？如果Y_N是它里面的元素的话，那么Y_N应该是一个事件才对啊，为什么说它是随机变量了？我看到一种写法是这样的Y_N=\cup_{k=1}^{\infty}(Y_n \cap {N=n})，如果这算作是 ...

13楼: Originally posted by jabile at 2014-02-25 12:00:26
一个随机变量X:\Omega\rightarrow R称为是\mathcal{F}可测的，若对任意A\in \mathcal{B}(R),f^{-1}(A)\in \mathcal{F}，记为X\in \mathcal{F}...

14楼: Originally posted by hubeizk at 2014-02-25 12:16:33
哦，还有这种说法，我大概明白了，那Y_n也是随机变量是吧？...

15楼: Originally posted by jabile at 2014-02-25 14:52:20
f\Omega,\mathal{F})\rightarrow (E,\mathcal{E})
称为是可测的，若\forall A\in \mathcal{E},f^{-1}(A)\in \mathcal{F}
，记为f\in \mathcal{F}/\mathcal{E}，若(E,\mathcal{E})是R上Borel域，就简记为f\in\m ...

16楼: Originally posted by jabile at 2014-02-25 14:53:49
f\Omega,\mathal{F})\rightarrow (E,\mathcal{E})...

15楼: Originally posted by jabile at 2014-02-25 14:52:20
f\Omega,\mathal{F})\rightarrow (E,\mathcal{E})
称为是可测的，若\forall A\in \mathcal{E},f^{-1}(A)\in \mathcal{F}
，记为f\in \mathcal{F}/\mathcal{E}，若(E,\mathcal{E})是R上Borel域，就简记为f\in\m ...

18楼: Originally posted by hubeizk at 2014-02-25 17:32:59
哦，大致明白了，可是这种简记一般不会让人引起混淆嘛？容易把f当成\mathcal{F}里的事件...

19楼: Originally posted by jabile at 2014-02-25 17:37:14
不会，随机事件本质上是0-1随机变量，所以是一致的...