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2h
comment Probability that after 10,000 steps (+-1) you'll end up at the origin. How to use Central Limit Theorem?
No, that's muddled. There is a weak version of de Moivre-Laplace that is a special case of CLT. The strong version of de Moivre-Laplace, that talks about the probability mass function rather than the cumulative distribution, is what we can use here.
8h
comment Probability that after 10,000 steps (+-1) you'll end up at the origin. How to use Central Limit Theorem?
On the other hand, you could use the de Moivre-Laplace theorem (e.g. in the form Wikipedia gives).
8h
comment Probability that after 10,000 steps (+-1) you'll end up at the origin. How to use Central Limit Theorem?
The correct calculation is that for even $n$, $C(n,n/2)/2^n \sim \sqrt{\dfrac{2}{n\pi}}$ using Stirling's approximation. As Did notes, this is not using central limit theorem.
10h
comment Are polynomials infinitely many times differentiable?
... but that's not what it means, it's just what happens in this case when you keep differentiating.
10h
comment $\frac{\partial^2 x}{\partial y^2}=\frac{1}{2}\frac{\partial}{\partial y}(\frac{\partial x}{\partial y})^2$
When you say $\partial f/\partial y$, are you considering $f$ to be a function of $x$ and $y$ (and maybe other variables)? Then both sides are $0$. But if $x$ is a function of $y$ (and maybe other variables), the equation is true only in some rather special cases.
10h
comment How do I solve for vector $P$ in the matrix equation $s=A'B^{-1}A$?
Sorry, misread the original question.
13h
comment Simplest way to integrate this expression : $\int_{-\infty}^{+\infty} e^{-x^2/2} dx$
The value of $\int_{-\infty}^\infty e^{-x^2/2}\; dx$ is just as famous.
17h
comment Is a limit of measure of a sequence of sets equal to measure of limit of the sequence of sets?
Lebesgue dominated convergence theorem.
17h
comment removing a factor when the summation equals zero
It doesn't. If that's what it's saying, it's wrong.
Jun
26
comment Integral Equation Unknown Limits
@AlexS Not really. In an integral equation the unknown is a function appearing in the integrand. Here it seems the integrand is known, the unknown is an endpoint of the interval of integration.
Jun
26
comment When can I take $\lim_{a \to 0}\int_a^T u$?
Yes, if $u \ge 0$ and continuous the improper integral exists iff $u$ is integrable on $[0,T]$.
Jun
26
comment What is the relation between the linear combination and modular arithmetic?
Modular arithmetic is not "in a field" if the modulus is not prime.
Jun
26
comment Alternative Quadratic Formula
If $b > 0$ and $|4ac|$ is much smaller than $b^2$, then computing $\dfrac{2c}{-b-\sqrt{b^2-4ac}}$ suffers from a lot less roundoff error than $\dfrac{-b+\sqrt{b^2-4ac}}{2a}$.
Jun
26
comment limit of a product of independent random variables
By the Strong Law of Large Numbers, $Z_n/n \to -1$ almost surely. If $a_n < r < s < e$ for sufficiently large $n$, $(\log \prod a_n)/n < \log s < 1$, and so $(\log |Y_n|)/n < \ldots$
Jun
25
comment Find a second solution of the given differential equation.
I did not use $y_1$.
Jun
25
comment Is it a solution of Heat Equation?
Yes, (with my correction) it's a solution for the heat equation in the form that I wrote it.
Jun
25
comment Find a second solution of the given differential equation.
The fastest way is to notice that only derivatives of $y$ appear in the equation, not $y$ itself, so it's obvious that constants are solutions.
Jun
25
comment Find a second solution of the given differential equation.
Since this is a linear homogeneous equation, you can multiply a solution by any nonzero constant and get another solution. You're free to write the second solution as $1$ or $-1$ or $2015$; all are equally correct.
Jun
25
comment How does Infinity really work, and the relation with ∞ and space
You might look at iep.utm.edu/infinite
Jun
25
comment Determine the steady state from a discrete dynamic system with only the eigenvalue of the diagonalized transition matrix.
$A^k = P D^k P^{-1}$. Consider each nonzero element of $D^k$...