I can't seem to wrap my head around the types of sums used in probability theory, and here is a classic example. Section 6.1 of this article:(adsbygoogle = window.adsbygoogle || []).push({});

http://en.wikipedia.org/wiki/Expect...ution_taking_only_non-negative_integer_values

The first line of the proof, what is going on here? I know how summation works, except I can't see the relation between the LHS and the RHS

Then the last step, I can't see how the second summation goes away and is just replaced by a j!

I always get confused by this notation but when I understand it intuitively I am much more comfortable.

Thanks

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# Discrete distribution taking only non-negative integer values

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