# Questions tagged [expected-value]

Questions about the expected value of a random variable.

6,605 questions
Filter by
Sorted by
Tagged with
20 views

17 views

### The expectation and variance of the $\infty$-norm $\|\hat{\mu}-\mu\|_{\infty}$. [closed]

Suppose the i.i.d. sample $\{X_i\}_{i=1}^n$ follows a $p$-dimensional normal distribution $N_p(\mu, \Sigma)$, where $\Sigma>0$ and the eigenvalues of $\Sigma$ is bounded away from $0$ and $\infty$. ...
51 views

### Calculating individual mean from a sum of random variables.

Suppose that I have $X_1, X_2, X_3$ as a sequence of independent random variables with $E(X_i)<+\infty$ but not identically distributed, so they have different $E(X_1)\neq E(X_2)\neq E(X_3)$. Let's ...
32 views

### Calculating the expected value of clients served by two shops

I need some help to solve this problem: There are two shops and each can serve at most one client per period. The number of clients that arrive in each period to each shop is \begin{cases} 0 &...
35 views

17 views

### Persistent Markov Chain with infinite mean recurrence time

Given a Markov Chain $(X_n)_{n \ge 0}$, state $i \in S$ is defined as persistent if $P(T_i < \infty | X_0 = i) = 1$ (where $T_i$ is the first passage time to state $i$). Moreover, the mean ...
40 views

### Does $E[x_i\mid y_i] = 0 \implies \operatorname{cov}(x_i, y_i) = 0$?
$$E[x_i\mid y_i] = 0 \implies \operatorname{cov}(x_i, y_i) = 0\,?$$ I am wondering if the above statement holds true. The LHS is saying that given any value of $y_i$, the expected value of $x_i$ is ...
I have the following expression and I am having trouble understanding it $$\frac{\int y f_{Y,X}(y,x) dy}{\int y f_Y(y) dy}$$ Where $f_{Y,X}(y,x)$ is the joint density function of random variables $X$ ...