Sample Distribution

[mot4201]

Hi,

I have a problem that puzzles me. It's a theorem that is listed in an
inference book. Here it is:

If a random sample with size two is taken from a distribution with
positive variance and if the sum and the difference of the two
components of that sample are independent, then the distribution from
which the sample is taken is a normal distribution.

Could anybody tell me how to proceed in order to prove that?

Thank you

Mark,


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