Expectation function

• To: mathgroup at smc.vnet.net
• Subject: [mg120244] Expectation function
• From: paulvonhippel at yahoo <paulvonhippel at yahoo.com>
• Date: Thu, 14 Jul 2011 21:19:46 -0400 (EDT)

```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.

```

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