Example where $Cov(x_i, \epsilon_i) = 0$ and $E[\epsilon] =0$ yet $E[\epsilon | X] \neq 0$?
97109
Can zero covariance and zero expectation imply zero conditional expectation?
90666
Finding an example of a discrete-time strict local martingale.
131026
Covariance and independence?
42212
iterated expectation conditional on two variables
150910
Covariance and contravariance real world example
132392
Properties of Expectation
433
Problem about jointly continuous and linearity of expectation.
25654
E[X| X>Y] for independent X, Y ~ N(0,1)
153393
Is there a *simple* example showing that uncorrelated random variables need not be independent?
128875
Expectation values of the position operator is equal to zero in case of even potentials?
67489
How to show that $E[(\hat\theta -\theta)^2]<Var(\bar X)=\dfrac{1}{n}$?
83873
Find $E(|X-Y|^a)$ where $X$ and $Y$ are independent uniform on $(0,1)$
115028
If $e=\lim\limits_{x\to \infty} (1+x^{-1})^x$, why doesn't $e=1$?
85818
$E(|X-Y|)$ for $X$, $Y$ i.i.d and uniform on $[0,1]$
83464
Conditional expectation of $\mathbb{E}(X - Y | (X, Y)\in\mathcal{A})$
27788
Why is the expected value $E(X^2) \neq E(X)^2$?
14063
Is a non-negative random variable with zero mean almost surely zero?