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Hi all, this is an exerpt from Feller's Intro to Probability.
He was describing how the discrete binomial equation hn(kh) where h = $\displaystyle \sqrt {2/v}$, derived earlier can fit into the actual normal curve n where n(x) is given by:
$\displaystyle n(x) ={1 \over {\sqrt{2 \pi}}} e^{-0.5x^2} $
From my understanding, the underlined text is comparing the points at k and k+1 ( all are multiplied by a factor of h) with the Riemann discrete sum of k and k+1.
Since we are dealing with a downward slope, the Riemann sum (being a rectangle) is always larger than the actual area under the curve.
But why is the Riemann equation being compared isn't n(hn) but hn(hn)?
Hope that there are ppl who have read the text and can discuss this point here.
Thanks!
please ignore post.
I just realised the point that:
the area under hn(hx) from a to b = area under n(x) from ah to bh.
which is the gist of the paragraph.
