query: Equality of conditional expectations
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: 79024
negative_passages.text: the derivation of E(X|X)
negative_passages.docid: 152642
negative_passages.text: Expectation of Minimum of $n$ i.i.d. uniform random variables.
negative_passages.docid: 118253
negative_passages.text: Conditional expectation of $X$ given $\sin(X)$
negative_passages.docid: 122199
negative_passages.text: conditional expectation under bivariate normal
negative_passages.docid: 94636
negative_passages.text: Conditional distribution of exponential random variable conditioned on sum of i.i.d. exponential random variables
negative_passages.docid: 156092
negative_passages.text: Existence of independent and identically distributed random variables.
negative_passages.docid: 144359
negative_passages.text: A random variable that induces a $\sigma$-algebra the same as the one in the sample space
negative_passages.docid: 132392
negative_passages.text: Properties of Expectation
negative_passages.docid: 66991
negative_passages.text: One confusion over conditional expectation
negative_passages.docid: 148004
negative_passages.text: Expected prediction error - derivation
negative_passages.docid: 142840
negative_passages.text: Open axioms of equality
negative_passages.docid: 45492
negative_passages.text: Using Joint Distributions and conditional probabilities
negative_passages.docid: 25654
negative_passages.text: E[X| X>Y] for independent X, Y ~ N(0,1)
negative_passages.docid: 131180
negative_passages.text: When Jensen's inequality is equality
negative_passages.docid: 132595
negative_passages.text: $\sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{\operatorname{Tr}[\rho M]}{\operatorname{Tr}[\sigma M]}$ satisfies Data Processing Inequality
negative_passages.docid: 136694
negative_passages.text: Probabilistic Proof of Kraft-Mcmillan Inequality