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I have an expression $f(x)$, outputting strictly real numbered values $\geq 0$ corresponding to the probability of some event, where $\sum_{i=0}^{N} f(i) = 1$. When is it true that $\int_{i=0}^{N} f(i) d(i) = 1$? If this isn't true, how do I find the average value of $f$, or points where $\sum_{i=0}^{r}f(i)=y$ for $0 \leq y \leq 1$?

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    you wanna talk about $\int_{i=0}^{N} f(i)~di = 1$ ?2012-12-22
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    @Argha Yes, that's right.2012-12-22
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    Since your sum is **1** you can use $\int$ instead of $\sum$ for moderate large **n**.2012-12-22
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    @Argha My example fails regardless of $N$, you can set it to be infinite. I'd like to understand when this happens...?2012-12-22

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