Re: Expectation function

*To*: mathgroup at smc.vnet.net*Subject*: [mg120288] Re: Expectation function*From*: Darren Glosemeyer <darreng at wolfram.com>*Date*: Sat, 16 Jul 2011 05:43:59 -0400 (EDT)*References*: <201107150119.VAA23653@smc.vnet.net>

On 7/14/2011 8:19 PM, paulvonhippel at yahoo wrote: > I'm having a little trouble with the Expectation function in > Mathematica. I'd like to calculate the expectation of the product of > two independent variables. One has a standard normal distribution, the > other is distributed F. It's obvious that the expectation is zero, but > when I put the problem to Mathematica, all it does is echo the input. > Here's the simplest way I've put the question: > > Expectation[Z* F, F \[Distributed] FRatioDistribution[df, df], Z \ > [Distributed] NormalDistribution[0, 1]] > > Mathematica just echoes the input. I try adding some assumptions to > ensure that the variance of the F distribution is defined. > > Assuming[{df>= 3, df \[Element] Integers}, %] > > And Mathematica just echoes the input again. > > The other way to do this is to use TransformedDistribution and then > use Mean. I get the same result that way. > > The problem I actually want to solve is more complicated, of course, > but today I'll settle for solving the easier version. Many thanks for > any pointers. > The \[Distributed] statements need to be given in a list. With that modification, you'll get a correct result: In[1]:= Expectation[Z*F, {F \[Distributed] FRatioDistribution[df, df], Z \[Distributed] NormalDistribution[0, 1]}] Out[1]= 0 Darren Glosemeyer Wolfram Research

**References**:**Expectation function***From:*paulvonhippel at yahoo <paulvonhippel@yahoo.com>