Let be two i.i.d. random variables and is a variable. How to show that the distribution functions of and are identical?

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- Jun 11th 2011, 11:35 PMSambitshowing two distribution functions identical
Let be two i.i.d. random variables and is a variable. How to show that the distribution functions of and are identical?

- Jun 12th 2011, 02:27 AMMoo
Hello,

Nice problem :p

Let's call Z the rv .

We'll use mgf's and conditional expectations :

(expectations with the rv's in subscript mean that it's the expectation with respect to the distributions of the rv's in the subscript - to avoid any confusion)

And then comparing to the other one...

Same mgf implies same distribution. (Happy)

P.S. : being of the lazy type, some steps have been put in silent mode :D