R*****s
发帖数: 28 | 1 Let X and Y be two gaussian random variables with N(0,a) and N(0,b),
respectively. X and Y are correlated with correlation \rho.
What is E (X − Y |2X + Y ) |
t******m
发帖数: 255 | 2 E(X|Y)=\mu_x+Cov(X,Y)*Var(Y)^{-1}(y-\mu_y)
【在 R*****s 的大作中提到】
: Let X and Y be two gaussian random variables with N(0,a) and N(0,b),
: respectively. X and Y are correlated with correlation \rho.
: What is E (X − Y |2X + Y )
|
n****e
发帖数: 629 | 3 你问的是E(X-Y|2X+Y)?
这种题可以化成矢量做。X,Y就是长度为a,b的矢量，夹角\theta满足\cos(\theta)=\
rho
然后你这里要求的 就是X-Y在2X+Y方向的投影
作个内积就出来了
【在 R*****s 的大作中提到】
: Let X and Y be two gaussian random variables with N(0,a) and N(0,b),
: respectively. X and Y are correlated with correlation \rho.
: What is E (X − Y |2X + Y )
|
d*j
发帖数: 13780 | 4 这样的题目，思路就是把前面的那一部分 分解成 俩部分，一个和后面的无关， 一个就
是后面那个自己
【在 R*****s 的大作中提到】
: Let X and Y be two gaussian random variables with N(0,a) and N(0,b),
: respectively. X and Y are correlated with correlation \rho.
: What is E (X − Y |2X + Y )
|
R*****s
发帖数: 28 | 5 Could you elaborate on how you get this equation?
thanks.
【在 t******m 的大作中提到】
: E(X|Y)=\mu_x+Cov(X,Y)*Var(Y)^{-1}(y-\mu_y)
|
t******m
发帖数: 255 | 6 define W=X-cov(x,y)var(y)^-1* Y. You can prove that W and Y are
independent and W|Y=N(mu_x-cov(x,y)var(y)^-1*mu_y, var(x)*var(y)^-
1*cov(x,y)). Then the result is proven.
【在 R*****s 的大作中提到】
: Could you elaborate on how you get this equation?
: thanks.
|
s***e
发帖数: 267 | 7 If (X,Y) jointly normal, then conditional distribution is also normal. A
simple way to remember this formula is the following:
consider mean is 0 case. E[Y|X] is like doing regression, regress Y against
X. And in this case, the best regression is linear. If you remember the
least square solution beta's formula, plug in and making sure the dimension
matches, then you will get the solution...
【在 t******m 的大作中提到】
: define W=X-cov(x,y)var(y)^-1* Y. You can prove that W and Y are
: independent and W|Y=N(mu_x-cov(x,y)var(y)^-1*mu_y, var(x)*var(y)^-
: 1*cov(x,y)). Then the result is proven.
|
s***e
发帖数: 267 | 8 What is DB?
【在 R*****s 的大作中提到】
: Let X and Y be two gaussian random variables with N(0,a) and N(0,b),
: respectively. X and Y are correlated with correlation \rho.
: What is E (X − Y |2X + Y )
|
A*****s
发帖数: 13748 | 9 德银
【在 s***e 的大作中提到】
: What is DB?
|
t******m
发帖数: 255 | 10 True
against
dimension
【在 s***e 的大作中提到】
: If (X,Y) jointly normal, then conditional distribution is also normal. A
: simple way to remember this formula is the following:
: consider mean is 0 case. E[Y|X] is like doing regression, regress Y against
: X. And in this case, the best regression is linear. If you remember the
: least square solution beta's formula, plug in and making sure the dimension
: matches, then you will get the solution...
|
|
|
a*******h
发帖数: 123 | 11 这种题都需要额外假设 X 和 Y 是 joint normal 吗？
否则的话不知道 X 和 Y 的联合分布判断不出来谁和谁是独立的吧？
【在 R*****s 的大作中提到】
: Let X and Y be two gaussian random variables with N(0,a) and N(0,b),
: respectively. X and Y are correlated with correlation \rho.
: What is E (X − Y |2X + Y )
|
o****e
发帖数: 80 | 12 这道题目的答案是不是
[2a-rho-b]x/{sqrt[4a+b+4rhosqrt(ab)]}/{4a+b+2rhosqrt(ab)}
我怀疑我算错了，哪位帮算一下正确答案？
【在 R*****s 的大作中提到】
: Let X and Y be two gaussian random variables with N(0,a) and N(0,b),
: respectively. X and Y are correlated with correlation \rho.
: What is E (X − Y |2X + Y )
|
g******e
发帖数: 352 | 13 V = X-Y
W = 2X+Y
分别算出V, W的variance和correlation ratio,然后用楼上的公式得到
E(V|W) = W*[2a-b-rho*sqrt(ab)]/[4a+b+4rho*sqrt(ab)]
【在 o****e 的大作中提到】
: 这道题目的答案是不是
: [2a-rho-b]x/{sqrt[4a+b+4rhosqrt(ab)]}/{4a+b+2rhosqrt(ab)}
: 我怀疑我算错了，哪位帮算一下正确答案？
|
f*****s
发帖数: 141 | 14 E[Y|X] is the best predictor of Y given X. When the distribution is normal,
then the best linear predictor is the best predictor.
against
dimension
【在 s***e 的大作中提到】
: If (X,Y) jointly normal, then conditional distribution is also normal. A
: simple way to remember this formula is the following:
: consider mean is 0 case. E[Y|X] is like doing regression, regress Y against
: X. And in this case, the best regression is linear. If you remember the
: least square solution beta's formula, plug in and making sure the dimension
: matches, then you will get the solution...
|
f*****s
发帖数: 141 | 15 Can you elaborate how to use this approach to this problem? I tried but can
not get it. Thx.
个就
【在 d*j 的大作中提到】
: 这样的题目，思路就是把前面的那一部分 分解成 俩部分，一个和后面的无关， 一个就
: 是后面那个自己
|
o****e
发帖数: 80 | 16 thank you, you are right. i found my error.
【在 g******e 的大作中提到】
: V = X-Y
: W = 2X+Y
: 分别算出V, W的variance和correlation ratio,然后用楼上的公式得到
: E(V|W) = W*[2a-b-rho*sqrt(ab)]/[4a+b+4rho*sqrt(ab)]
|
o****e
发帖数: 80 | 17 i am also curious, except the dummy calculation, any other smart ways, like
daj said...
but don't understand how to do it..
can
在 daj (肉丝炒饭--小吵肉fan) 的大作中提到: 】
个就
【在 f*****s 的大作中提到】
: Can you elaborate how to use this approach to this problem? I tried but can
: not get it. Thx.
:
: 个就
|
d*j
发帖数: 13780 | 18 以前 dr. shreve 教的。。。。
我现在都忘记了， 哈哈
懒得看了 :(
like
【在 o****e 的大作中提到】
: i am also curious, except the dummy calculation, any other smart ways, like
: daj said...
: but don't understand how to do it..
:
: can
: 在 daj (肉丝炒饭--小吵肉fan) 的大作中提到: 】
: 个就
|
p*****k
发帖数: 318 | 19 ogtree, the clever way has already been mentioned couple of
times in this thread. if it's still not clear, see:
http://www.wilmott.com/messageview.cfm?catid=26&threadid=76839 |
