Intereting Posts

Closed- form of $\int_0^1 \frac{{\text{Li}}_3^2(-x)}{x^2}\,dx$
Proof of Cauchy Riemann Equations in Polar Coordinates
Is $e^x=\exp(x)$ and why?
Failure of Choice only for sets above a certain rank
Find the limit of $\lim_{n\rightarrow\infty}(\frac{1}{2}+\frac{3}{2^2}+…+\frac{2n-1}{2^n})$
If a function is measurable with respect to the completion then it is equal to some measurable (with respect to the measure space) function a.e.
Is $[a, a)$ equal to $\{a\}$ or $\varnothing$?
How to tackle a recurrence that contains the sum of all previous elements?
Can a function be increasing *at a point*?
$k$-space tensor integral in statistical physics
Simple resource for Lagrangian constrained optimization?
Union of a countable collection of open balls
Fundamental theorem of Algebra using fundamental groups.
What is the laplace transform and how is it performed? (detailed explanation)
How can I find the value of $\ln( |x|)$ without using the calculator?

Is there any difference between the two? I have not met any formal definition of the support of a random variable. I know that for the function $f$ the support is a closure of the set $\{y:\;y=f(x)\ne0\}$.

- Direct proof that $\pi$ is not constructible
- Prove that $ \lim\limits_{n \to \infty } \sum\limits_{k=1}^n f \left( \frac{k}{n^2} \right) = \frac 12 f'_d(0). $
- weak convergence of product of weakly and strongly convergent $L^{2}$ sequences in $L^{2}$
- $fg\in L^1$ for every $g\in L^1$ prove $f\in L^{\infty}$
- Showing that if $\lim_{x\to\infty}xf(x)=l,$ then $\lim_{x\to\infty}f(x)=0.$
- What does recursive cosine sequence converge to?
- Bounds on $f(k ;a,b) =\frac{ \int_0^\infty \cos(a x) e^{-x^k} \, dx}{ \int_0^\infty \cos(b x) e^{-x^k}\, dx}$
- Uniform $L^p$ bound on finite measure implies uniform integrability
- Prove that the only sets in $R$ which are both open and closed are the empty set and $R$ itself.
- Convex function with non-symmetric Hessian

The support of the probability distribution of a random variable $X$ is the set of all points whose every open neighborhood $N$ has the property that $\Pr(X\in N)>0$.

It is more accurate to speak of the support of the *distribution* than that of the support of the random variable.

The complement of the support is the union of all open sets $G$ such that $\Pr(X\in G)=0$. Since the complement is a union of open sets, the complement is open. Therefore the support is closed.

- Proving Gaussian Integers are countable
- Infinite series of nth root of n factorial
- Is a proof still valid if only the writer understands it?
- Pigeonhole Principle Question: Jessica the Combinatorics Student
- Which meromorphic functions are logarithmic derivatives of other meromorphic functions?
- About phi function
- Normal subgroups of $S_n$ for $n\geq 5$.
- Proving Gauss' polynomial theorem (Rational Root Test)
- A non-negative matrix has a non-negative inverse. What other properties does it have?
- Probability density function of $X^2$ when $X$ has $N(0,1)$ distribution
- $A$ is normal and nilpotent, show $A=0$
- Robertson-Seymour fails for topological minor ordering? (I.e., subgraphs and subdivision)
- prove $\sqrt{a_n b_n}$ and $\frac{1}{2}(a_n+b_n)$ have same limit
- Integers in biquadratic extensions
- Automorphism in the special linear algebra $\mathfrak{sl}_2(F)$