Any answer on MSE is a distraction of me from my work.

## My appreciated answers

If $X$ is Gaussian, prove that $X-\lfloor X \rfloor \sim U(0,1)$ as its variance becomes large

About the inequality $x^{x^{x^{x^{x^x}}}} \ge \frac12 x^2 + \frac12$

Prove that two random variates must be negatively correlated

Why do the triangular numbers initially form long cycles mod $2^k$?

Given the sequence $a_1=1$,$a_{n+1}=1+\frac{n}{a_n}$, does the sequence $a_n+n-a_n^2$ converges?

What is the asymptotic expansion of $x_n$ where $x_{n+1} = x_n+1/x_n$?