joyhu

第1题不要受干扰，概率就是1/2，因为生男生女是独立事件

jxwahc

引用:

原帖由 joyhu 于 2008-3-13 05:58 PM 发表
第1题不要受干扰，概率就是1/2，因为生男生女是独立事件

独立事件和条件概率并不矛盾呀。条件概率P(X|Y)=P(XY)/P(Y)=0.5/0.75=2/3中，P(XY)=0.5和P(Y)=0.75就是根据独立事件得来的。

xfx

Problem 1's answer is 2/3. Conditional prob.

poorsol

引用:

原帖由 Lazlow 于 2008-3-7 09:00 PM 发表
1. 2/3
2. 6/7, 1/7
3. exp(v/2)
4. (ln3)/2

这个答案是对的

renjizhao

引用:

原帖由 jxwahc 于 2008-3-13 06:28 PM 发表

独立事件和条件概率并不矛盾呀。条件概率P(X|Y)=P(XY)/P(Y)=0.5/0.75=2/3中，P(XY)=0.5和P(Y)=0.75就是根据独立事件得来的。

For me, since we already know there is a boy(not only one boy, this is not a word game I believe), so just forget this boy, and for the other child we get 0.5 probabilty to have a girl.
It's quite intuitive. Just like one couple have a boy and the wife is pregnent again, with one child in her body, . The probability that that one is a girl is 0.5. You can't say that your first child is a boy, so the second one is more likely to be a girl.

So, why the conditional probabilty thing is wrong?
I think you may took Y as there is at least one boy, in that case P(Y) should be one, since it is already been told. 0.5/1=0.5, voila.

Otherwise, I really don't know how you get the number 0.75

zhudianyao

1.第二个孩子的概率与第一个孩子是男孩还是女孩是无关的，即独立。可以通过条件概率算出来，这个结论应该记住。

poorsol

有一个是女孩和第二个是女孩最后的结论应该是不同的。

ouyanggoon

引用:

原帖由 renjizhao 于 2008-5-13 11:25 PM 发表


For me, since we already know there is a boy(not only one boy, this is not a word game I believe), so just forget this boy, and for the other child we get 0.5 probabilty to have a girl.
It's qui ...

Obviously should be :  P(X|Y)=P(XY)/P(Y)=0.25/0.5= 0.5 ,  how come some of you guys get P(XY)=0.5 & P(Y)=0.75 ?
Weird.............

zhouxingchi

引用:

原帖由 jxwahc 于 2008-3-7 03:05 PM 发表

能否说明一下第1题的解答过程，为何这不是一个条件概率？
另外关于2，3，4。我也有不同答案。
2是6/7和1/7。因为 (vol of portfolio)^2 = (x*vol1)^2 + [(1-x)*vol2]^2 + 2*p*x*(1-x)*vol1*vol2。对x求导，令导数 ...

3. X is log normal, if you check the formula for the expectation of log normal distribution, E(X) = e^{mu + sigma^2/2}. in which log(x) follows N(mu, sigma). In this case, mu = 0, sigma^2 = v. so answer is e^(v/2)

Slayer_MM

引用:

原帖由 jxwahc 于 2008-3-13 06:28 PM 发表

P(XY)=0.5和P(Y)=0.75就是根据独立事件得来的。

If P(Y) = 0.75, how come P(XY) = 0.5?

if X and Y are independent, then P(XY) = P(X) P(Y) = ?????