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June 6th, 2017, 04:11 PM  #1 
Member Joined: Apr 2017 From: PA Posts: 34 Thanks: 0  A die is loaded so that the probability of a face coming up is proportional to the nu
A die is loaded so that the probability of a face coming up is proportional to the number on that face. The die is rolled with outcome X. Find V (X) and D(X). How would you find the Expected value E(x) and the variance V(x) for this problem? For this problem, I knew that the probability for each outcome would be x/21. And I knew that X=1,2,3,4,5,6 so I took the expected value of 1× (1/21)+2× (2/21)+3×(3/21)+4×(4/21)+5×(5/21)+6×(6/21) and got 3, then I tried to find the variance by using V(x)=E(x^2)(E(x))^2=12, but the answer was 3/4 for V(x). 
June 6th, 2017, 05:26 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,255 Thanks: 507 
Redo your arithmetic. Mean=91/21.

June 6th, 2017, 05:49 PM  #3 
Member Joined: Apr 2017 From: PA Posts: 34 Thanks: 0 
So is the procedure right?

June 6th, 2017, 09:19 PM  #4 
Senior Member Joined: Sep 2015 From: CA Posts: 1,264 Thanks: 650  

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coming, die, face, loaded, probability, proportional 
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