symbolic Variance - Integration
- To: mathgroup at smc.vnet.net
- Subject: [mg84585] symbolic Variance - Integration
- From: jess <cuaxie at gmail.com>
- Date: Sat, 5 Jan 2008 04:40:16 -0500 (EST)
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