query: In conditional expectation, why is $E(X \mid X)=X$ instead of $E(X \mid X)=E(X)$?
positive_passages.docid: 134696
positive_passages.text: How can I show that the conditional expectation $E(X\mid X)=X$?
negative_passages.docid: 125080
negative_passages.text: Why is uniform prior on log(x) equal to 1/x prior on x?
negative_passages.docid: 29565
negative_passages.text: Conditional Expectation of Bernoulli R.V.
negative_passages.docid: 79024
negative_passages.text: the derivation of E(X|X)
negative_passages.docid: 156019
negative_passages.text: Expectation formula of an integrable random variable
negative_passages.docid: 140790
negative_passages.text: Prove that $E(X) = \int_{0}^{\infty} P(X>x)\,dx = \int_{0}^{\infty} (1-F_X(x))\,dx$.
negative_passages.docid: 27788
negative_passages.text: Why is the expected value $E(X^2) \neq E(X)^2$?
negative_passages.docid: 17754
negative_passages.text: Intuitive Understanding of the constant "$e$"
negative_passages.docid: 83464
negative_passages.text: Conditional expectation of $\mathbb{E}(X - Y | (X, Y)\in\mathcal{A})$
negative_passages.docid: 23946
negative_passages.text: Prove the definitions of $e$ to be equivalent
negative_passages.docid: 42193
negative_passages.text: Show that $E(Y^p)=\int_{0}^{\infty}px^{p-1}P(Y\geq x)dx$
negative_passages.docid: 141540
negative_passages.text: What is wrong with the following "proof" that $e=1$?
negative_passages.docid: 118253
negative_passages.text: Conditional expectation of $X$ given $\sin(X)$
negative_passages.docid: 25652
negative_passages.text: Intuitive explanation for $\mathbb{E}X= \int_0^\infty 1-F(x) \, dx$
negative_passages.docid: 118414
negative_passages.text: What is the relationship between the function $\mathbb{E}(Y \mid X = x)$ and linear regression?
negative_passages.docid: 5350
negative_passages.text: Explain why $E(|X|^p)=p\int_{0}^{\infty}y^{p-1}P(|X|>y) dy$
negative_passages.docid: 122603
negative_passages.text: How does $\mathcal E(\rho)=\mathrm{Tr}_{env}[U(\rho\otimes\rho_{env})U^\dagger]$ turn into $P_0\rho P_0+P_1\rho P_1$?