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Is the median of the F-distribution with m and n degrees of freedom decreasing in n, for any m?

From experiments it looks like it might be, but I have been unable to prove it.

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Is n the denominator degrees of freedom? – Michael Chernick Sep 25 '12 at 22:19
@Michael yes it is – fra Sep 25 '12 at 22:48
Have you looked at tables of the F distribution. I don't think the tables give percentiles close to 50 but maybe looking at the 25th and the 75th with a gross interpolation would give you an idea whether or not it is true. I am sure that there are software packages that will give the cumulative F or its inverse and you can see the result from that. – Michael Chernick Sep 26 '12 at 0:10
@Michael yes from software calculation it seems like the result is true. But I am looking for a proof! – fra Sep 27 '12 at 21:09
If it is not true the tables could tell you by giving you just one counterexample. If you need precision you can do numerical integration to a desired level of accuracy. – Michael Chernick Sep 27 '12 at 21:13

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