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September 26th, 2018, 04:46 PM  #1 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 637 Thanks: 85  Standard Deviations and Standard Deviations of Reciprocals
If the standard deviation of A, B, and C is greater than the standard deviation of X, Y, and Z, what does that say about the standard deviation of 1/A, 1/B, and 1/C compared to the standard deviation of 1/X, 1/Y, and 1/Z? A, B, C, X, Y, and Z are rational numbers > 1.

September 27th, 2018, 01:32 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,704 Thanks: 670 
Why are you asking about two sets of three variables? One each is enough for the question.

September 27th, 2018, 03:39 PM  #3 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 637 Thanks: 85 
I'm comparing the odds for soccer games with three possible outcomes. I attached a file. The odds are 3.20/1 for Team 1 winning, 3.05/1 for a draw, and 2.10/1 for Team 2 winning. I take the reciprocals of odds to get probabilities. 1/3.20 + 1/3.05 + 1/2.10 > 1, so to make probabilities you divide each reciprocal by the sum of the reciprocals.

September 28th, 2018, 01:18 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,704 Thanks: 670 
The odds are just wrong, unless they are bookie odds, which include bookie profit. To get probabilities you need to add 1 to the numerators before taking reciprocals, but it doesn't add up to 1, therefore leaving a bookie profit.


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deviations, reciprocals, standard 
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