1
vote
1answer
61 views

If $Y=\sum_{n=1}^\infty X_n$ diverges, is $Y$ a random variable?

Let $X_n$ be random variables. By definition, a random variable is a function from the probability space to $\mathbb{R}$. If $Y=\sum_{n=1}^\infty X_n$ diverges, is it correct to call $Y$ a random ...
0
votes
1answer
105 views

How to describe a “sum percentile”

I have values $w_1 \ge w_2 \ge ..\ge w_n$. I want to know the the highest possible threshold $w^{th}$ so that $$ \sum_{i:w_i>w^{th}} w_i \ge \alpha \sum_{i=1}^n w_i $$ where $\alpha \in [0,1]$. ...
4
votes
1answer
248 views

What is this operation on random variables called?

Let $X$ be a random variable and let $N$ be a discrete random variable which takes values in the non-negative integers. Let $X_1, X_2, ...$ be a sequence of i.i.d. random variables with the same ...