| Science Forum Index » Economy Forum » fourth moment of normal variable |
|
Page 1 of 1 |
|
| Author |
Message |
| oercim |
 Posted: Fri Dec 09, 2005 10:41 am |
|
|
|
Guest
|
Hello, let X is normaly distributed random variable with E(X)=0
and VAR(X)=S^2. According to an essay E(X^4)=S^4. There is not a proof
of this equality in the article. Is this equality realy true? How?
Thanks a lot. |
|
|
| Back to top |
|
|
|
| Robert Vienneau |
| Posted: Sat Dec 10, 2005 3:33 am |
|
|
|
Guest
|
In article <1134142860.406171.66790@f14g2000cwb.googlegroups.com>,
"oercim" <oercim@yahoo.com> wrote:
[quote:9bba785d2e]Hello, let X is normaly distributed random variable with E(X)=0
and VAR(X)=S^2. According to an essay E(X^4)=S^4. There is not a proof
of this equality in the article. Is this equality realy true? How?
[/quote:9bba785d2e]
I don't recall whether that's true. But in looking this up, one might
find it useful to know that the third moment about the mean is called
"skewness" and the fourth moment around the mean is called "kurtosis".
I think I recall that the kurtosis of a Gaussian-distributed random
variable is a constant.
--
Mostly economics: <http://www.dreamscape.com/rvien/#PublicationsForFun>
r c
v s a Whether strength of body or of mind, or wisdom, or
i m p virtue, are found in proportion to the power or wealth
e a e of a man is a question fit perhaps to be discussed by
n e . slaves in the hearing of their masters, but highly
@ r c m unbecoming to reasonable and free men in search of
d o the truth. -- Rousseau |
|
|
| Back to top |
|
|
|
| sinister |
| Posted: Wed Dec 14, 2005 6:30 am |
|
|
|
Guest
|
"oercim" <oercim@yahoo.com> wrote in message
news:1134142860.406171.66790@f14g2000cwb.googlegroups.com...
[quote:72dfdff7f6]Hello, let X is normaly distributed random variable with E(X)=0
and VAR(X)=S^2. According to an essay E(X^4)=S^4. There is not a proof
of this equality in the article. Is this equality realy true? How?
[/quote:72dfdff7f6]
I don't have a proof on paper, but presumably a scaling argument would show
that
E(X^4) = C*S^4
for some constant C. (Scaling argument---just write down the integral, and
use the method of substitution to "get the S out".)
Then all one has to do is compute C in the case of S=1.
[quote:72dfdff7f6]Thanks a lot.
[/quote:72dfdff7f6] |
|
|
| Back to top |
|
|
|
|
