I’d like to know if some results are known on the following type of random variables: for parameter $p\in[0,1]$ (for my purposes, $p < \frac{1}{2}$, and even $p \ll 1$) and $n \geq 1$, we let $X$ be a random variable following a Binomial$(n,p)$ distribution, and define $$Y \stackrel{\rm def}{=} \min(X, n-X).$$ Then, as a […]

I’m trying to decide which one to pick up to begin a self study of mathematics. One of the factors is how much content is covered and the amount of associated solved problems the book has. EDIT: Lets said my goal are go after something like this course doing it self studding. Pls, take just […]

I’m looking for a book containing the proof that for every Banach space E there is an index I so that E is a quotient space of $\ell_1(I)$. If I can’t find the book on google books, it would be great if you could give me the page number, because my paper is due tomorrow […]

I have encountered a number of situations where the solution of a PDE and a certain expectation associated to a Markov process are equal. Two examples include: The heat equation $u_t = \frac{1}{2} \Delta u$ with initial data $u(0,x)=f(x)$, considered on the whole space. Here the solution is given by $u(t,x)=\mathbb{E}(f(x+W_t))$ where $W_t$ is a […]

Let $X$ be a set. A lattice of subsets of $X$ is a subset of $\mathcal{P}(X)$ containing $\emptyset$ and $X$ and closed under finite intersection and finite union. Such a lattice is therefore a bounded distributive lattice. Let $X_0$ and $X_1$ be sets. Let $\mathcal{L}_0$ be a lattice of subsets of $X_0$ and let $\mathcal{L}_1$ […]

I heard that exist a branch of mathematics called wheel theory that extends the concept of commutative ring, and in it can be defined “division by zero”, I want to read about this stuff, but I can’t found any reference, so, anyone of you know a book about this?

Background: Due to some unfortunate sequencing, I have developed my abstract algebra skills before most of my linear algebra skills. I’ve worked through Topics in Algebra by Herstein and generally liked his approach to vector spaces and modules. Besides a very elementary course in linear algebra (where most of the time went towards matrix multiplication), […]

I came across this site and am wondering if there is a similar page for Mathematics or its sub-areas. Would be very nice if there is one such site which provides ‘canonical’ references for each sub area and preferably is editable like the Wikipedia system so that it reflects entire community’s opinion and not just […]

One could prove the following theorem in the smooth setting: Theorem Let $(M,m)$ be a $d$ dimensional $C^\infty$ manifold with smooth volume $m$. Let $\{F_i\}_{i=1}^k$ and $\{G_i\}_{i=1}^k$ be two systems of disjoint open subsets, satisfying $m(F_i)=m(G_i)$. Assume $\bar{F}_i$ and $\bar{G}_i$ are diffeomorphic to the $d$ dimensional closed ball in $\mathbb{R}^m$ for $i=1,\ldots k$. Then, given […]

Let “stochastic” matrix be the matrix whose rows sum to one and deterministic matrix be a stochastic matrix whose all rows consist of a one and zero. For example $\left [ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array} \right] $ is a deterministic […]

Intereting Posts

Proving that $\det(A) = 0$ when the columns are linearly dependent
Is it possible to simulate a floor() function with elementary arithmetic?
Proof of Non-Convexity
Permutations with duplicates
A simple mathematical expression for the periodic sequence $(1, -2, -1, 2, 1, -2, -1, 2,\dots)$
Why are removable discontinuities even discontinuities at all?
Image of the set of natural numbers under any function is denumerable.
For polynomial $f$, does $f$(rational) = rational$^2$ always imply that $f(x) = g(x)^2$?
A semigroup with identity having exactly one idempotent is a group
Does $i^i$ and $i^{1\over e}$ have more than one root in $$
Does the graph of a measurable function always have zero measure?
$W$ be an $m$-dimensional linear subspace of $\mathbb R^n$ such that $m\le n-2$ , then is it true that $\mathbb R^n \setminus W$ is connected?
In how many ways I can write a number $n$ as sum of $4$ numbers?
Basic Representation Theory
Is adjoint of singular matrix singular? What would be its rank?