Formula for the expectation $E|X|=\int_{0}^{\infty} P[|X|>t] dt$
14764
Explain why $E(X) = \int_0^\infty (1-F_X (t)) \, dt$ for every nonnegative random variable $X$
92569
Showing that ${\rm E}[X]=\sum_{k=0}^\infty P(X>k)$ for a discrete random variable
83464
Conditional expectation of $\mathbb{E}(X - Y | (X, Y)\in\mathcal{A})$
73517
conditional expectation of brownian motion
50163
Continuity of the  Ito integral
95123
General solution of expected value of E(f(X))?
88226
Limit of a stochastic integral
110961
Tail sum for expectation
149362
Prove that $ \mathbb{E}[XY] - \mathbb{E}[X] \mathbb{E}[Y] = \int_{- \infty}^\infty \int_{- \infty}^\infty (F(x,y)-F_X(x) F_Y(y)) \,dx\,dy,$
27705
Proof of $\int_{[0,\infty)}pt^{p-1}\mu(\{x:|f(x)|\geq t\})d\mu(t)=\int_{[0,\infty)}\mu(\{x:|f(x)|^p\geq s\})d\mu(s)$
71278
What is the expectation of the following random variable
68097
Prove $\int\limits_{0}^{\infty} \mathrm{exp}(-ax^{2}-\frac{b}{x^{2}}) \mathrm{d} x = \frac{1}{2}\sqrt{\frac{\pi}{a}}\mathrm{e}^{-2\sqrt{ab}}$
75902
Expectation of $\frac{1}{x+1}$ of Poisson distribution
16049
Fourier transform of $\int_{-\infty}^{t}f(t)\, dt$
25654
E[X| X>Y] for independent X, Y ~ N(0,1)
64844
Finding $E(|X_1|\ |\max |X_i| )$
81057
Evaluation of $\int_{\frac{1}{e}}^{\tan x}\frac{t}{1+t^2}dt+\int_{\frac{1}{e}}^{\cot x}\frac{1}{t(1+t^2)}dt$