Can E(Y/S) Be Less Than 1 in IID Random Variables?

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The discussion centers on the mathematical expectation of the ratio of two independent and identically distributed (i.i.d) positive random variables, S and Y. It establishes that E(Y/S) is always greater than or equal to 1, given that E(X) is finite. The participants explore the implications of this relationship and seek examples where E(Y/X) approaches positive infinity, emphasizing the need for a deeper understanding of the properties of expected values in the context of independent random variables.

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Mathematical Statistics~help please!

:cry:

Please help me with these question...

Let S and Y be i.i.d positive random variables with E(X)<infinity.
Show that E(Y/S) is greater or equal to 1. Give an example where

E(Y/X)=positive infinitiy...

I have no Idea where to begin...please help me..
 
Physics news on Phys.org
E(Y/S) = E(Y)(E1/S) since they are independent.What does it now boil down to showing? What results do you know that tell you when E(f(X)) > f(E(X)) for some function f?
 

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