"On the Internet, nobody knows you're a dog" is an adage about Internet anonymity which began as a cartoon caption by Peter Steiner and published by The New Yorker on July 5, 1993. The cartoon features two dogs: one sitting on a chair in front of a computer, speaking the caption to a second dog sitting on the floor listening to the first. As of 2011, the panel was the most reproduced cartoon from The New Yorker, and Steiner has earned over US$50,000 from its reprinting.
== History ==
Peter Steiner, a cartoonist and contributor to The New Yorker since 1979, said the cartoon initially did not get...
Consider a max heap tree with $100$ elements and a node from the same level is chosen randomly among all valid balanced heap trees with $n$ nodes. What is the probability that it is the $36^\text{th}$ smallest element______ .
My attempt:
(Please, find definition of Binary Heap on Wiki: https...
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I have a sum of the form:
$$S_n = \frac{1}{n} \sum_{i=0}^n \mathrm{e}^{n f(i/n)} g(i/n)$$
where $f(x)$ and $g(x)$ are smooth functions defined for $0\le x \le 1$. I am interested in the Asymptotic behaviour of $S_n$ as $n\rightarrow +\infty$.
What I have tried is to replace the sum by an integ...user84215
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What is the difference between
{some-expression}\over{another-expression}
and
\frac{some-expression}{another-expression}
?
Which is preferable?
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