Tagged Questions

For questions about the expectation of a random variable: computations, upper/lower bounds, etc.

15 views

Distributional convergence and expectations

I'm struggling with the following problem. Let $X_n$ be a sequence of non-negative random variables which are finite almost surely and all with expectation 1. Assume they converge in distribution ...
22 views

Detailed explanation needed for basic query regarding expectation

I need to find the expectation of following random variable $$g=[\log_2(\frac{1+x}{1+y})]^+$$ where $[x]^+=max(x,0)$ and both $x,y$ variables depend on variable $z$. I know the conditional pdf's and ...
40 views

Expectation and Variance of an Estimator

Imagene following equation holds \begin{align*} p_2=\int\limits_{-\infty}^{\Phi^{-1}(p)}\int\limits_{-\infty}^{\Phi^{-1}(p)} \frac{1}{2\pi\sqrt{1-\rho^2}}\exp\bigg({-\frac{1}{2}\frac{x^2-\rho xy+y^2}{...
30 views

How to find E(x) and Var(x) in this specific continuous probability distribution.

I've got into some confusion on continuous probability distributions, and everything related to it. This is the problem: Problem Image. I assume from the sketch that pdf is $f(x) = x$ for values of $x$...
30 views

Random walk on d-dimensional torus

I am reading the following paper: http://arxiv.org/pdf/1602.03849v2.pdf I will explain the general setup below. Let $x\in X=\mathbb{T}^d$, where $\mathbb{T}^d$ is the d dimensional torus. Let $\rho$ ...
40 views
+50

Expected score from threshold with number deletions

We play a game where a sequence of $n$ numbers is drawn uniformly from $[0,1]$, and we need to set a threshold $0\leq a\leq 1$. For every number that is at least our threshold, we get $a$ points but ...
21 views

Does this hold in every case, and if only this one, why? Expectation, mean of random variable.

Characteristic function of random variable $X$ let us denote as $f_X(t)$ and $EX$ it's mean or expectation. Does the following hold in all cases, because it keeps coming up and I don't know why it is ...
35 views

81 views

40 views

On the distribution and the moments of $\max\{1/\sqrt{U_1},…,1/\sqrt{U_n}\}$, where $(U_k)$ is i.i.d. uniform on $(0,1)$

Let $U_1,U_2,...$ denote an i.i.d. sequence of random variables with the uniform distribution on $[0,1]$. For every integer $n\geq1$, we set $M_n = \max\{1/\sqrt{U_1},...,1/\sqrt{U_n}\}$. a) Compute ...