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 Feb 22 awarded Yearling Aug 28 comment Poisson Distribution of Underfilled Bottles Perhaps you were to assume a total number $N$. A true Poisson distribution gives a non-zero probability to an arbitrarily high number of underfilled bottles. The case would need to be infinite if Poisson were appropriate. Aug 28 comment Poisson Distribution of Underfilled Bottles To elaborate on Michael Hardy's answer, if you were told the total number in the case, then you condition that the number of underfilled bottles is no larger than that total number. This process (conditioning on the total number) can be thought of as inverse to the standard "infinite size with fixed rate" limit which reduces a binomial distribution to its limiting a Poisson distribution. Aug 17 answered How to prove $\int\limits_0^1 {{x^m} \times {{(1 - x)}^n}dx} = \int\limits_0^1 {{x^n} \times {{(1 - x)}^m}dx}$ Aug 15 comment Solution to sde with specfic mean More generally the process $$dS_t = \Big(\mu + \frac{a}{t^{1-k}}\Big)\,S_t\,dt + \sigma \, dW_t$$ would have a mean $$\exp\Big(a\,\frac{t^{1-k}}{1-k} + \mu t\Big)\,S_0\,.$$ Aug 15 comment Solution to sde with specfic mean In the more general form you've added, you could get a stochastic process with the desired mean by considering $$dS_t = \Big(\mu + \frac{k}{t}\Big)\,S_t\,dt + \sigma \, dW_t$$. Aug 15 answered Solution to sde with specfic mean Aug 15 comment How is $\left|\frac{xy}{\sqrt{x^2+y^2}}\right| \leq \frac{\sqrt{|xy|}}{\sqrt{2}}$ Luckily others are happy to do the work for you... Aug 15 answered How is $\left|\frac{xy}{\sqrt{x^2+y^2}}\right| \leq \frac{\sqrt{|xy|}}{\sqrt{2}}$ Aug 15 revised Convolution can smooth an input function, is there an operation which bunches it up? added 70 characters in body Aug 15 answered Convolution can smooth an input function, is there an operation which bunches it up? Aug 15 comment examples for fibration not fibre bundle This is a repeat: mathoverflow.net/questions/119115/… Aug 12 comment How to show that $e^{-x}$ tends to $0$ when $x\to \infty$ if $e^{-x}$ is defined as the power series. Not quite sure I understand your point. Aug 11 answered How to show that $e^{-x}$ tends to $0$ when $x\to \infty$ if $e^{-x}$ is defined as the power series. Jul 15 awarded Yearling Jul 12 revised Distribution of minimum absolute value added 25 characters in body Jul 10 comment Distribution of minimum absolute value Glad to hear it! You could always upvote the answer and/or select it, too... Jul 9 revised Distribution of minimum absolute value added 296 characters in body Jul 9 answered Distribution of minimum absolute value Jun 30 revised Why is the commutator defined differently for groups and rings? deleted 3 characters in body