t******m
发帖数: 255 | 1 谁能说说怎么解这两道呀
let X1, X2 two random variable ~ N(0,1) with correlation rho. what is pdf
of Max(X1,X2)
what the solution to X^3-10^6x^2+x+1=0? |
a*******h
发帖数: 123 | 2 第二题没有有理根，只能大致猜一下三个根的范围，剩下用数值解。
（当然，记得求根公式的人除外）
【在 t******m 的大作中提到】
: 谁能说说怎么解这两道呀
: let X1, X2 two random variable ~ N(0,1) with correlation rho. what is pdf
: of Max(X1,X2)
: what the solution to X^3-10^6x^2+x+1=0?
|
z****i
发帖数: 406 | 3
一个根在10^6附近，两个在10^(-3)附近
【在 a*******h 的大作中提到】
: 第二题没有有理根，只能大致猜一下三个根的范围，剩下用数值解。
: （当然，记得求根公式的人除外）
|
n****e
发帖数: 2401 | 4 这不明摆着有一个根是0吗? 一眼就能看出来。
【在 t******m 的大作中提到】
: 谁能说说怎么解这两道呀
: let X1, X2 two random variable ~ N(0,1) with correlation rho. what is pdf
: of Max(X1,X2)
: what the solution to X^3-10^6x^2+x+1=0?
|
t******y
发帖数: 1100 | 5 我 ft。。。
【在 n****e 的大作中提到】
: 这不明摆着有一个根是0吗? 一眼就能看出来。
|
z****i
发帖数: 406 | |
n******r
发帖数: 1247 | 7 同问
【在 z****i 的大作中提到】
: 第一道题有没有什么简单的解法啊？
|
s*******s
发帖数: 1568 | 8 consider P(XY
【在 n******r 的大作中提到】
: 同问
|
n******r
发帖数: 1247 | 9 Is that P(max(X,Y)
Then use Y|X=x is N(/rho*x,1-/rho^2) and x
Finally integrate x from -inf to inf?
【在 s*******s 的大作中提到】
: consider P(XY
|
t*******e
发帖数: 172 | 10 I am wondering is it doable.
X,Y may not jointly normal distribution. If they are, this problem is just a
simple calculus question, however, if they are not, I do not think there is
a explicit solution.
【在 n******r 的大作中提到】
: Is that P(max(X,Y): Then use Y|X=x is N(/rho*x,1-/rho^2) and x: Finally integrate x from -inf to inf?
|
|
|
n******r
发帖数: 1247 | 11 if X and Y are both normal, then (X,Y) is joint normal and the pdf is
uniquely dertermined by x and y's pdfs and their correlation. The question
here is whether there is an elegant solution without getting into nasty
integration.
a
is
【在 t*******e 的大作中提到】
: I am wondering is it doable.
: X,Y may not jointly normal distribution. If they are, this problem is just a
: simple calculus question, however, if they are not, I do not think there is
: a explicit solution.
|
t******m
发帖数: 255 | 12 True
question
【在 n******r 的大作中提到】
: if X and Y are both normal, then (X,Y) is joint normal and the pdf is
: uniquely dertermined by x and y's pdfs and their correlation. The question
: here is whether there is an elegant solution without getting into nasty
: integration.
:
: a
: is
|
t*******e
发帖数: 172 | 13 I am doubt about that
there is an example tell us, X, Y are not independenet N(0,1) with
correlation 0.
If your statement is true, then correlation 0 => independent? Since you
assume there are jointly normal which correlation 0=>independent.
The example is on Page 82 of Shreve's volume 2.
If jointly normal, nothing difficult about calculus, just P(X<=a,Y<=a), and
then take derivate of a, you do not need do tedious calculus.
【在 n******r 的大作中提到】
: if X and Y are both normal, then (X,Y) is joint normal and the pdf is
: uniquely dertermined by x and y's pdfs and their correlation. The question
: here is whether there is an elegant solution without getting into nasty
: integration.
:
: a
: is
|
n******r
发帖数: 1247 | 14 for joint bivariate normal, correlation=0 => independent
This is true
and
【在 t*******e 的大作中提到】
: I am doubt about that
: there is an example tell us, X, Y are not independenet N(0,1) with
: correlation 0.
: If your statement is true, then correlation 0 => independent? Since you
: assume there are jointly normal which correlation 0=>independent.
: The example is on Page 82 of Shreve's volume 2.
: If jointly normal, nothing difficult about calculus, just P(X<=a,Y<=a), and
: then take derivate of a, you do not need do tedious calculus.
|
t*******e
发帖数: 172 | 15 Totally do not know your point. What is your claim?
What I claimed: this problem not doable without joint normally assumption.
You try to convince me any two normal distribution are jointly normal(am I
right?), which I am quite doubt about. e.g. I give you two random variable
which have correlation 0, but not indepent. This example show that there are
two N(0,1) are not jointly normal.
On the page 8 of the following notes, it maybe give the exactly argument.
http://www.athenasc.com/Bivariate-Nor
【在 n******r 的大作中提到】
: for joint bivariate normal, correlation=0 => independent
: This is true
:
: and
|
a*******h
发帖数: 123 | 16 这个说的不对。。
如果 X 和 Y 都是 Normal， (X, Y) 并不一定是 Joint Normal。Joint Normal 要求
对任意常数 a 和 b， aX + bY 都是 Normal。
比如这个例子：
http://en.wikipedia.org/wiki/Normally_distributed_and_uncorrelated_does_not_imply_independent
里面的 X 和 Y 都是 N(0,1), 但是 X + Y 压根都不是一个连续随机变量 (不存在 pdf
)。
【在 n******r 的大作中提到】
: if X and Y are both normal, then (X,Y) is joint normal and the pdf is
: uniquely dertermined by x and y's pdfs and their correlation. The question
: here is whether there is an elegant solution without getting into nasty
: integration.
:
: a
: is
|
a***r
发帖数: 594 | 17 agree.
my first try would be that if there are roots near 0 then one can drop the x
^3 term as an approximation. so look at the roots of 10^6*x^2+x+1=0, they
are indeed very small, so they should be very close to the root of the
original.
【在 z****i 的大作中提到】
: 第一道题有没有什么简单的解法啊？
|
B*****9
发帖数: 48 | 18 这个怎么会有一个根在10^6 附近？
另外两个应该在 10^(-3)和 -10^(-3)附近吧
【在 z****i 的大作中提到】
: 第一道题有没有什么简单的解法啊？
|
