Re: symbolic Variance - Integration
- To: mathgroup at smc.vnet.net
- Subject: [mg84596] Re: symbolic Variance - Integration
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Sun, 6 Jan 2008 05:55:36 -0500 (EST)
- References: <flnjkg$jve$1@smc.vnet.net>
Hi,
a) Mathematica will not split
Integrate[f[x] + g[x], x]
because for certain functions
Integrate[f[x] + g[x], x] may be
convergent while
Integrate[f[x], x]+Integrate[g[x], x]
may be indeterminate.
b) you must program your own rules to handle
expectation values of random variables.
@article{citeulike:1051201,
author = {Goodman, Leo A. },
citeulike-article-id = {1051201},
journal = {Journal of the American Statistical Association},
keywords = {product-of-rv},
number = {297},
pages = {54--60},
priority = {2},
title = {The Variance of the Product of K Random Variables},
url =
{http://links.jstor.org/sici?sici=0162-1459\%28196203\%2957\%3A297\%3C54\%3ATVOTPO\%3E2.0.CO\%3B2-X},
volume = {57},
year = {1962}
}
may help you ..
Regards
Jens
Regards
Jens
jess wrote:
> Hi there!
>
> I came across a formula for variance of a product of random variables
> X and Y. The formula was given under the assumption that X and Y are
> independent, and there was a remark that without this assumption the
> formula is very complicated.
>
> I thought to myslef, okay i have mathematica on my pc so let's see how
> complicated it is...
>
> Then i realized that the only way to calculate variance in mathematica
> is to:
> - give a list of points (i.e. uniform discrete distribution)
> - give a specific distribution, and say, its parameters ( eg. normal
> or gamma dist.)
>
> so there is no way to make a symbolic calculation using an arbitrary
> random variable...
>
> Huuuh, so i thought okay variance and expected value are nothing but
> integrals so i can try to define my own function using integrals (i do
> not want to consider just discrete or continues random variables)...
>
> and then i realized i can't even obtain that integration is additive
> i.e. from
>
> Integrate[f[x] + g[x], x]
>
> i could not get
>
> Integrate[f[x], x] + Integrate[g[x], x]
>
> (so my function for expected value would not even tell me that
> EValue(X+Y) = EValue(X) + EValue(Y)... not to mention about
> calculating Variance( XY) = ????.... )
>
> Coming back to my original problem: how to make mathematica do this
>
> In[1] =E[XY]
> Out[1]=E[X]E[Y]+Cov[XY]
>
> and further
>
> In[2]=Var[XY]
> In[2]= ??????????
>
> Please I would appreciate absolutely any comment at all...
>
> Jess
>