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Mar
25
comment Euler characteristic equation for circle
i wonder if approximating the circle with a regular $n$-gon will work...
Mar
25
comment Counting nonidentity elements in a group
@snulty thanks, corected
Mar
23
comment Proving Discreteness of the Harmonic numbers
@almagest we were using a different definition. I was taught that discrete means countable. You are using a different definition...
Mar
22
comment Can Levenberg-Marquardt be used to find a local minimum of a function?
MATLAB certainly uses Levenberg-Marquardt for straight minimization
Mar
22
comment Sum of $\sum \limits_{n=0}^{\infty} \frac{1}{(kn)!}$
sum diverges at $k=0$ and conveges to $\cos (ix)$ for $k=2$
Mar
22
comment a minoration of $P(X>x)$ with $X~N(0,1)$
could you please update the question with your own thoughts on the problem and we will be happy to guide you further.
Mar
20
comment Any simpler expression for$\frac{\sum_{k=2}^{n-2}{k\big(\sum_{i=0}^{n-2}\frac{(-1)^i}{i!}\big)}}{n\sum_{i=0}^{n}\frac{(-1)^i}{i!}}$
note your numerator is just a product of 2 sums, the first is arithmetic series $\sum_k k$ and the second is close to $1/e$, so the second factor will roughly cancel the sum in the denominator...
Mar
18
comment Show that $\exp(-\lambda x) \cdot\exp(\lambda x)=1$ using the power series
see another update2...
Mar
18
comment Covering space of a graph is again a graph - why??
unfortunately not... haven't seen this in 3 years...
Mar
18
comment Covering space of a graph is again a graph - why??
@Zero unfortunately not
Mar
16
comment Central limit theorem for distribution peak rather than mean
yes, thank you very much
Mar
16
comment How to find this area by integration?
are you looking for area and not volume? so surface area then?
Mar
16
comment Central limit theorem for distribution peak rather than mean
i couldn't get what you are asking -- the CLT does not depend on the underlying distribution of the $X_i$, it can be asymmetric or even discrete.
Mar
15
comment endpoints convergence after integrating/mutiplying /subtracting power series
i think for 1,2, the endpoints don't have to be checked; since it diverges for the first series, the result will diverge also unless it's a special power series, e.g. the zero function :). (4) is correct, (3) I am not sure.
Mar
15
comment Why are complex numbers allowed to be combine like this?
i altered your fractions on the left to give you an example of how to format, but your RHS is incomprehensible, can you alter it into readable form that is mathematiccally equivalent of the LHS to make your point?
Mar
14
comment Martingale property for two stochastic processes
$e^{B_t}$ has lognormal distribution
Mar
14
comment Inequality involving triangle
yes, you can have an equilateral triangle -- then all inequalities hold as equalities, so $4\sqrt{3}$ is sharp
Mar
14
comment Martingale property for two stochastic processes
$B_t-B_s|\mathcal{F}_s$ has normal distribution with mean $0$ and variance $t-s$
Mar
13
comment Constructing a partition and sigma algebras
what is $\sigma(E)$?
Mar
11
comment Integrate $\int \frac{ e^{\tan^{-1}x}}{(1+x^2)^2} dx$
you want to use a substitution $u = \tan^{-1} x$ so $du = \frac{dx}{1+x^2}$, not sure how to get rid of the second $(1+x^2)$ in the denominator