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1d
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.
1d
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
Jun
30
revised Why is the commutator defined differently for groups and rings?
added 51 characters in body