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So, I found this proof of the variance of a discrete uniform distribution on Wikipedia (https://en.wikibooks.org/wiki/Statistics/Distributions/Discrete_Uniform) and I'm having trouble understanding what exactly was done from line 6 to 7. Here's a print of it:

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How did (b-a)² in the first term become (n-1)² and (a-b) in the second term become (n-1)? Thanks very much in advance.

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    If you look a bit further up, you find that it says "Let $n=b-a+1$ be the number of possibilities.". Rearranging gives $n-1=b-a$. – 2017-02-05
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    Oh, I had forgotten about that. Thank you – 2017-02-05

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