query: Some proof involving expectation
positive_passages.docid: 662
positive_passages.text: If $E[X|Y]=Y$ almost surely and $E[Y|X]=X$ almost surely then $X=Y$ almost surely
negative_passages.docid: 141685
negative_passages.text: Why is expectation defined by $\int xf(x)dx$?
negative_passages.docid: 75902
negative_passages.text: Expectation of $\frac{1}{x+1}$ of Poisson distribution
negative_passages.docid: 64844
negative_passages.text: Finding $E(|X_1|\ |\max |X_i| )$
negative_passages.docid: 57170
negative_passages.text: Intuitive explanation of the tower property of conditional expectation
negative_passages.docid: 134696
negative_passages.text: How can I show that the conditional expectation $E(X\mid X)=X$?
negative_passages.docid: 90796
negative_passages.text: Inequality Regarding e
negative_passages.docid: 95415
negative_passages.text: proof relating to limit definition of e
negative_passages.docid: 118195
negative_passages.text: How does one prove that $e$ exists?
negative_passages.docid: 118253
negative_passages.text: Conditional expectation of $X$ given $\sin(X)$
negative_passages.docid: 63218
negative_passages.text: Is conditional expectation with respect to two sigma algebra exchangeable?
negative_passages.docid: 25654
negative_passages.text: E[X| X>Y] for independent X, Y ~ N(0,1)
negative_passages.docid: 34916
negative_passages.text: Conditional expectation equals random variable almost sure
negative_passages.docid: 72735
negative_passages.text: Understanding the proof of a formula for $p^e\Vert n!$
negative_passages.docid: 123844
negative_passages.text: conditional expectation: an implication
negative_passages.docid: 105145
negative_passages.text: Show that $\mathbb{E}\left(\bar{X}_{n}\mid X_{(1)},X_{(n)}\right) = \frac{X_{(1)}+X_{(n)}}{2}$
negative_passages.docid: 38324
negative_passages.text: Show that $E(X)=\int_{0}^{\infty}P(X\ge x)\,dx$ for non-negative random variable $X$