       TransformedDistribution

• To: mathgroup at smc.vnet.net
• Subject: [mg121145] TransformedDistribution
• From: paulvonhippel at yahoo <paulvonhippel at yahoo.com>
• Date: Wed, 31 Aug 2011 06:05:13 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```I am seeking the mean of a variable which includes the weighted sum of
two chi-square variables. When I ask the question the obvious way
(below), Mathematica takes a long time to return an unwieldy answer
that is undefined for most values of n1 & n2. I'd be grateful if
someone could suggest a more tractable way to pose the problem.

Here's a simplified version of the problem:

Mean[
TransformedDistribution[
Sqrt[\[FormalX]2 n2 + \[FormalX]1 n1 ], {\[FormalX]1 \[Distributed]
ChiSquareDistribution[n1], \[FormalX]2 \[Distributed]
ChiDistribution[n2]}]]

And whatI really want to do is a little more complicated:

TransformedDistribution[\[FormalX]2 Sqrt[((\[FormalX]3 +
den) n + \[FormalX]1 Subscript[n, obs])/(
den (-1 + n) n)] \[Sigma], {\[FormalX]1 \[Distributed]
ChiSquareDistribution, \[FormalX]2 \[Distributed]
ChiDistribution[-1 + Subscript[n,
obs]], \[FormalX]3 \[Distributed]
ChiSquareDistribution[-1 + Subscript[n, mis]]}]

```

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