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October 29th, 2017, 01:27 PM  #1 
Member Joined: Nov 2016 From: Kansas Posts: 65 Thanks: 0  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: 6,378 Thanks: 542 
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 
Member Joined: Nov 2016 From: Kansas Posts: 65 Thanks: 0  
October 30th, 2017, 07:12 AM  #4 
Newbie Joined: Oct 2017 From: US Posts: 11 Thanks: 0 
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 
Global Moderator Joined: May 2007 Posts: 6,378 Thanks: 542  

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expected, random variable 
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