# Tagged Questions

23 views

### Proving some properties about the expected first order statistic (maximum) with respect to sample size.

Question: Consider $n$ random variables $x_1, x_2,\cdots x_n\sim \mathcal{N}(0,1)$. The expected value of the $i$th order statistic (the maximum) can be written as ...
35 views

### How to calculate $\int\limits_{-\infty}^{+\infty} \frac{n-1}{\alpha}\Phi(\frac{x}{\alpha})^{n-2}\phi(\frac{x}{\alpha})^2dx$?

I was working on a research project that involves taking the integral of \frac{n-1}{\alpha}\int\limits_{-\infty}^{+\infty} ...
25 views

### Normal Distribution while finding sigma

I was reading some things about normal distribution and saw this problem in a text a couple days ago. I know it might be a little advanced for me at the moment, but I was wanted to know if someone can ...
Suppose there is a vector of jointly normally distributed random variables $X \sim \mathcal{N}(\mu_X, \Sigma_X)$. What is the distribution of the maximum among them? In other words, I am interested in ...
Is there an exact or good approximate expression for the expectation, variance or other moments of the maximum of $n$ independent, identically distributed gaussian random variables where $n$ is large? ...