Intereting Posts

Dulac's criterion and global stability connection
What are Belgium's chances on getting a medal at the 400m finals, given that they have 2 of the 8 athletes?
the Nordhaus-Gaddum problems for chromatic number of graph and its complement
The union of growing circles is not homeomorphic to wedge sum of circles
Generators of $GL_n(\Bbb Z)$ and $GL_n(\Bbb Z_p)$
Another quadratic Diophantine equation: How do I proceed?
Property (ii) of increasing functions in Chung's “A Course in Probability Theory”
Proving the Schwarz Inequality for Complex Numbers using Induction
prove that $A(n) : \left(\frac n3\right)^n\lt n!\lt \left(\frac{n}{2}\right)^n$ for all $n\ge 6$
How can you find $P(\frac{X}{Y-X}<0)$ if $X\sim Geometric(p)$ and $Y\sim Bernoulli(p)$
Generalisation of the identity $\sum\limits_{k=1}^n {k^3} = \bigg(\sum\limits_{k=1}^n k\bigg)^2$
Super palindromes
For $a=\cos(2\pi/n)$, show that $ = \ldots$
Topology proof: dense sets and no trivial intersection
Prove that $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n$

If we have a Poisson point process with rate $\lambda$ and we keep each of its point with probability $p$, we obtain another Poisson point process with rate $\lambda p$. Does this result holds for a general Renewal point process? i.e.,

If in a renewal point process with rate $\lambda$, we keep each point with probability $p$ independently, do we obtain another renewal point process?

- Conditional probabilties in the OR-gate $T=A\cdot B$ with zero-probabilities in $A$ and $B$?
- What is the distribution of a random variable that is the product of the two normal random variables ?
- Law of Large Numbers, a confusion
- Probability that two random numbers are coprime
- What is the Kolmogorov Extension Theorem good for?
- Taking Seats on a Plane

- PDF of area of convex hull of four random points in square
- Why does this expected value simplify as shown?
- Calculating conditional entropy given two random variables
- Is there a simple way to illustrate that Fermat's Last Theorem is plausible?
- Strange definitions about basic probability - need clarification
- Finding moment generating functions for a dice roll
- Is it correct to say that ($\color{red}{(} \limsup |W_k|/k\color{red}{)} \le 1) \supseteq \limsup \color{red}{(}|W_k|/k \le 1\color{red}{)}$?
- Expected number of turns for a rook to move to top right-most corner?
- Exact probability of random graph being connected
- Uniform distribution on the surface of unit sphere

Suppose $\{X_{n,k}\}$ are i.i.d. with mean $\lambda^{-1}<\infty$ and $\{\gamma_n\}$ are i.i.d. with $\mathsf{Geo}(p)$ distribution. Then the sequence $$Y_n := \sum_{j=1}^{\gamma_n} X_{n,j} $$ is i.i.d. and thus defines a renewal sequence with mean $$\mathbb E[Y_1] = \mathbb E[X_{1,1}]\mathbb E[\gamma_1]=(\lambda p)^{-1} $$

(by Wald’s identity), or equivalently “rate” $\lambda p$.

- Eigenvalues of linear operator $F(A) = AB + BA$
- Combinatorial Proof
- Why is the derivative of a circle's area its perimeter (and similarly for spheres)?
- Is $x^2-y^2=1$ Merely $\frac 1x$ Rotated -$45^\circ$?
- Prove that the field F is a vector space over itself.
- if $A$ has Lebesgue outer measure $0$ then so does $B=\left\{x^2: x\in A \right\}$
- Show that $ℤ^{m}$ is a subgroup (and a free abelian group) of $ℤ^{n}$ for all $m≤n$
- How do you prove triangle inequality for this metric?
- Prove that $\sqrt 2 +\sqrt 3$ is irrational.
- Why aren't these loops homotopic?
- EigenValues and EigenVectors in PCA?
- Deriving an expression for $\cos^4 x + \sin^4 x$
- why does infinitesimal lifting imply triviality of infinitesimal deformations?
- Every Hilbert space has an orthonomal basis – using Zorn's Lemma
- Can mathematical definitions of the form “P if Q” be interpreted as “P if and only if Q”?