Intereting Posts

Derivation of Frey equation from FLT
Prove that even + odd is odd.
Looking for a Simple Argument for “Integral Curve Starting at A Singular Point is Constant”
When is the group of quadratic residues cyclic?
Indefinite Integral with “sin” and “cos”: $\int\frac{3\sin(x) + 2\cos(x)}{2\sin(x) + 3\cos(x)} \; dx $
How to compute rational or integer points on elliptic curves
Can a basis for a vector space $V$ can be restricted to a basis for any subspace $W$?
How to compute infinite series $\sum_{n=0}^{\infty} ne^{-n}$
XOR properties in set of numbers
Vector path length of a hypotenuse
Evaluation of $\int_{0}^{\frac{\pi}{2}}\frac{\sin (2015x)}{\sin x+\cos x}dx$
Interval of definition of the solutions of $\dot x=e^x\sin x$
Regarding $e$ in $\lim\limits_{x \to a}{^{\psi(x)}} = e^{\lim\limits_{x \to a}{\psi(x)}}$
For $f$ entire and $\{f(kz) : k \in \mathbb{C}\}$ a normal family, prove that $f$ is a polynomial.
Cardinality of the set of all (real) discontinuous functions

For which $N \in \mathbb{N}$ is there a probability distribution such that $\frac{1}{\sum_i X_i} (X_1, \cdots, X_{N+1})$ is uniformly distributed over the $N$-simplex? (Where $X_1, \cdots, X_{N+1}$ are accordingly distributed iid random variables.)

- Time to reach a final state in a random dynamical system (answer known, proof unknown)
- Some case when the central limit theorem fails
- First hitting time for a brownian motion with a exponential boundary
- Independence and Conditional Independence between random variables
- Sum of random variable
- Probability distribution for the perimeter and area of triangle with fixed circumscribed radius
- Expectation of maximum of arithmetic means of i.i.d. exponential random variables
- What is the relationship of $\mathcal{L}_1$ (total variation) distance to hypothesis testing?
- Beta function derivation
- Filtration of stopping time equal to the natural filtration of the stopped process

Take a look at the Wikipedia article on the Dirichlet distribution. In particular the Dirichlet distribution with $\alpha_i = 1$ for all $i$ is the uniform distribution on the simplex. Furthermore, the Dirichlet distribution can be generated by taking $X_1, \ldots, X_n$ to be independent gamma random variables with the right choice of paramters, and then $Y_i = X_i/(X_1 + \cdots + X_n)$. In the particular case you’re asking about, you can take the $X_i$ to all be exponential random variables with the same mean.

- Cardinality of the set of permutations of a set $ A $
- Weierstrass Approximation Theorem for continuous functions on open interval
- Prove $ \frac 1 2 \cdot \frac 3 4 \cdot \frac 5 6 \cdots \frac{2n-1}{2n} < \frac 1 {(2n+1)^{0.5}} $ .
- What is the relation between analytical Fourier transform and DFT?
- Math without infinity
- How do I count the subsets of a set whose number of elements is divisible by 3? 4?
- Separately continuous functions that are discontinuous at every point
- Funny thing. Multiplying both the sides by 0?
- Can every real number be represented by a (possibly infinite) decimal?
- Question about Conditional Expectation
- Is this field extension finite?
- How to prove that $\prod_{n=0}^\infty \frac{(4n+2)^2}{(4n+1)(4n+3)}=\sqrt{2}$
- A question on generalization of the concept of derivative
- Explanation on arg min
- Let $a$ be a quadratic residue modulo $p$. Prove $a^{(p-1)/2} \equiv 1 \bmod p$.