Intereting Posts

Determine: $S = \frac{1}{2}{n \choose 0} + \frac{1}{3}{n \choose 1} + \cdots + \frac{1}{n+2}{n \choose n}$
Distance between point and linear Space
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
Continuity and sequential continuity
Dirac delta and non-test functions
Dividing open domains in $\mathbb R^2$ in parts of equal area
About subsets of finite groups with $A^{-1}A=G$ or $AA^{-1}=G$?
minimum and maximum problem
What are the rings in which left and right zero divisors coincide called?
$n \mid (a^{n}-b^{n}) \ \Longrightarrow$ $n \mid \frac{a^{n}-b^{n}}{a-b}$
Sum of truncated normals
finding the combinatorial sum
Prove that Brownian Motion absorbed at the origin is Markov
Intuitively, why does Bayes' theorem work?
Given point and tangent line

I am a probability theory beginner. The expression for the variance of a random variable $x$ (of a random process is

$$\sigma^2 = E(x^2) – (\mu_{x})^2$$

If $E(x^2) = (\mu_{x})^2$, then $\sigma^2 = 0$. Can this happen ? Can a random variable have a density function whose variance (the second central moment alone) is $0$ (other than the dirac delta function).

- Understanding the definition of a random variable
- Continuity of the Characteristic Function of a RV
- Convergence in law and uniformly integrability
- Showing that the event: $X$ is continuous on $
- Normal approximation of tail probability in binomial distribution
- What does it mean for a theorem to be “almost surely true”, in a probabilistic sense? (Note: Not referring to “the probabilistic method”)

- How can I show that the “binary digit maps” $b_i : [0,1) \to \{0,1\}$ are i.i.d. Bernoulli random variables?
- Minimum / Maximum and other Advanced Properties of the Covariance of Two Random Variables
- How to physically model/construct a biased coin?
- Conditional mean on uncorrelated stochastic variable 2
- Joint cdf and pdf of the max and min of independent exponential RVs
- probability density of the maximum of samples from a uniform distribution
- Expected Number of Convex Layers and the expected size of a layer for different distributions
- A Brownian motion $B$ that is discontinuous at an independent, uniformly distributed random variable $U(0,1)$
- A variant of Kac's theorem for conditional expectations?
- Recast the scalar SPDE $du_t(Φ_t(x))=f_t(Φ_t(x))dt+∇ u_t(Φ_t(x))⋅ξ_t(Φ_t(x))dW_t$ into a SDE in an infinite dimensional function space.

The variance

$$

E(X^2)-E(X)^2=E(X-E(X))^2

$$

is equal to $0$ if and only if $X$ is equal to $E(X)$ in all of its support. This can only happen if $X$ is equal to some constant with probability $1$ (known as a degenerate distribution).

- There are at least three mutually non-isomorphic rings with $4$ elements?
- Find all solutions to $x^3+(x+1)^3+ \dots + (x+15)^3=y^3$
- 30 positive integers
- Should I understand a theorem's proof before using the theorem?
- Riemann integrable function
- Fundamental solution to Laplace equation on arbitrary Riemann surfaces
- “Orientation” of $\zeta$ zeroes on the critical line.
- Chebyshev polynomial question
- Product of spheres embeds in Euclidean space of 1 dimension higher
- Show that if $A^{n}=I$ then $A$ is diagonalizable.
- Let $(f_n)_{n\in\mathbb{N}} \rightarrow f$ on $[0,\infty)$. True or false: $\lim_{n\to\infty}\int_0^{\infty}f_n(x) \ dx = \int_0^{\infty}f(x) \ dx.$
- Algebraic closure for $\mathbb{Q}$ or $\mathbb{F}_p$ without Choice?
- Limit of factorial function: $\lim\limits_{n\to\infty}\frac{n^n}{n!}.$
- A five-part problem that uses ends and the Cantor set to prove that there are $c$ non-homeomorphic connected open subsets of $\mathbb{R}^2$
- Series Proof $\sum_{k=1}^n (1/k) > \ln(n+1)$