mrnobody

### Questions (27)

 3 Find all random variables $X$ such that if $Y$ is $N(0,1)$ and independent from $X$, then $X+Y$ and $\frac{1}{3}X+2Y-1$ have the same distribution 3 Find $\lim_{n \rightarrow \infty} \int_0^n (1+ \frac{x}{n})^{n+1} \exp(-2x) \, dx$ 3 Existence of some differentiable function 3 Show that $\frac{X_1+\dots+X_n}{n}$ converges to $\infty$ a.s. for $X_n \sim U([0,n])$ independent 2 Find $\lim_{n \rightarrow \infty}\frac{1}{n} \int_{1}^{\infty} \frac{\mathrm dx}{x^2 \log{(1+ \frac{x}{n})}}$

### Reputation (190)

This user has no recent positive reputation changes

 0 Convergance of some series of random variables

### Tags (32)

 0 probability-theory × 11 0 proof-verification × 3 0 convergence × 5 0 multivariable-calculus × 3 0 limits × 5 0 weak-convergence × 3 0 probability × 4 0 integration × 2 0 lebesgue-integral × 3 0 law-of-large-numbers × 2

### Accounts (3)

 Mathematics 190 rep 11 silver badge1111 bronze badges Mathematica 1 rep 11 bronze badge Stack Overflow 1 rep