My Math Forum Expected Value

 October 29th, 2017, 01:27 PM #1 Member   Joined: Nov 2016 From: Kansas Posts: 73 Thanks: 1 Expected Value X and Y are independent positive random variables with the same distribution, and the finite expected value µ: 1) E[(X)/(X+Y)] = 1/2 Any proof?
 October 29th, 2017, 02:18 PM #2 Global Moderator   Joined: May 2007 Posts: 6,641 Thanks: 625 Off hand: E[(x)/(X+Y)]=E[(y)/(X+Y)] E[(X+Y)/(X+Y)]=1, so each term =1/2.
October 29th, 2017, 07:52 PM   #3
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Quote:
 Originally Posted by mathman Off hand: E[(x)/(X+Y)]=E[(y)/(X+Y)] E[(X+Y)/(X+Y)]=1, so each term =1/2.
What wrong with the following argument:
E[(X)/(X+Y)]=E[X]/E[X+Y]=1/2

 October 30th, 2017, 07:12 AM #4 Newbie   Joined: Oct 2017 From: US Posts: 13 Thanks: 1 1. E[(X)/(X+Y)] = E[(Y)/(X+Y)] 2. E[(X)/(X+Y)] + E[(Y)/(X+Y)] = E[(X+Y)/(X+Y)] =1 Therefore: E[(X)/(X+Y)] = 1/2
October 30th, 2017, 04:50 PM   #5
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Quote:
 Originally Posted by ZMD What wrong with the following argument: E[(X)/(X+Y)]=E[X]/E[X+Y]=1/2
You haven't proved anything. It is like saying a=a, therefore a=1/2

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