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1h
reviewed Leave Open Finding the circumradius of an isosceles triangle
1h
reviewed Leave Open How can we evaluate this tough integral?
1h
awarded  Enlightened
1h
answered A polynomial $f(x)$ and its behavior as $f(t)>5$
1h
reviewed Leave Open Problems relating conditional probability
2h
comment If $(1+x+x^2)^{25} =\sum^{50}_{r=0} a_r x^r$ then …
Thank you. It is not clear whether one should be congratulated or pitied.
4h
revised If $(1+x+x^2)^{25} =\sum^{50}_{r=0} a_r x^r$ then …
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4h
answered If $(1+x+x^2)^{25} =\sum^{50}_{r=0} a_r x^r$ then …
5h
comment Taylor series example
Just mistake of algebra. The two approaches are the same. It would be better to expand $(e^{-x}-1)^2$ as $e^{-2x}-2e^{-x}+1$, write down the Taylor series and add. That will give you easily a formula for the sum to any number of powers.
6h
reviewed Leave Open What is the distribution of Z=min(X,Y)
8h
comment What is the distribution of Z=min(X,Y)
Of the two current answers, I think it is Graham Kemp/s that it is better to accept, because of the "Another approach" part.
9h
comment What is the distribution of Z=min(X,Y)
Happens fairly often, the computed answer shouts that one is missing a better way. Unlike you I had earplugs on.
9h
reviewed Reopen Levy-Ottaviani's inequality
9h
comment What is the distribution of Z=min(X,Y)
I like the second approach, conceptual not computational.
9h
revised What is the distribution of Z=min(X,Y)
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revised What is the distribution of Z=min(X,Y)
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10h
answered What is the distribution of Z=min(X,Y)
10h
comment let $D_n$ be the number of permutations of $\{1,2,3,…n\}$ which leave no element fixed.
I notice Srinivas K has sketched a proof of the identity your book mentions.
10h
comment let $D_n$ be the number of permutations of $\{1,2,3,…n\}$ which leave no element fixed.
The one I wrote is correct, as is the Inclusion/Exclusion formula of your comment. Kaj Hansen in an unfortunately deleted answer was giving hints toward that. You will find an explanation of the recurrence you mention (as well as the more computationally useful recurrence in my answer) in the Wikipedia article on derangements.
11h
reviewed Leave Open Find $\int_0^{2\sqrt{\pi}}\int_{x/2}^{\sqrt{\pi}}\sin(y^2)dydx$