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Jun
16
comment Limit approach to finding $1+2+3+4+\ldots$
The similar limits you're computing need more care because it looks like you're just trying to swap the limit with the sum, which is in fact wrong because you need some kind of uniform bound the terms whose sum also converges.
Jun
15
asked Distribution proportional to size
Jun
14
comment Custom equation guidance
Can you please give some context? What is rotating? The Earth?
Jun
14
comment Solving for $a_j$ such that $\sum_j {a_j}^k = c_k$ for some given $c_k$
For starters, given a solution set $a_j$, you can arbitrarily set $a_j=0$ and then shift over the original solution (assuming the solution is absolutely convergent).
Jun
14
comment Stopping times and expectation for the symmetric random walk
The way to interpret the formula is that if $\tau_{-m}=\infty$, which happens with possibly some positive probability, then $1/(1+r)^{\tau_{-m}}=0$
Jun
14
answered Determining what distribution a given random variable has.
Jun
14
comment Question about “weird” transformation
For the first part, the transformation is a map from polynomials to polynomials so it's linear in polynomials. That is $\psi(p+q)=\psi p+\psi q$ for polynomials $p,q$.
Jun
14
comment Does this particular limit exist?
en.wikipedia.org/wiki/Euler%E2%80%93Maclaurin_formula
Jun
13
revised Prove that matrices with property commute
edited body
Jun
13
answered Two combinatorial identities
Jun
9
comment Generalized criterion for positive definiteness of real symmetric matrices
Sylvester's Criterion: en.wikipedia.org/wiki/Sylvester%27s_criterion
Jun
9
awarded  Nice Answer
Jun
9
comment Why does a symmetric matrix have a complete set of eigenvectors and eigenvalues?
Google is your friend: quandt.com/papers/basicmatrixtheorems.pdf
Jun
8
comment How many tickets can you sell for a plane?
The inequality is to be solved for the largest $n\geq 144$, which looks to be 158. Perhaps the book used some abomination of a gaussian approximation.
Jun
8
comment Roots of a polynomial over a finite field
Can you prove it for $k=1,2$?
Jun
7
answered Differentiation always easy?
Jun
4
comment How to prove that a vector is Gaussian
This is elementary if you show that $Y$ is a Gaussian implies $bY$ and $a+Y$ are Gaussian for any constants $a,b$.
Jun
3
comment sigma algebra generated by a collection of r.v
Yes, exactly, combined with the fact that it's the smallest sigma-algebra.
Jun
3
comment sigma algebra generated by a collection of r.v
Generate the r.h.s. via multidimensional rectangles and show that each rectangle is contained in the l.h.s.
Jun
3
comment sigma algebra generated by a collection of r.v
Use the definition: it's the smallest sigma-algebra such that $X_1,\cdots,X_n$ are measurable. Thus, show that either sigma algebra is contained in one-another. It might help to show that you can generate the latter sigma algebra by unions of multidimensional rectangles.