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How can I prove that E[X + Y |X,Y ] = E[X|Y ] + E[Y |X]?

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#probability-theory #conditional-expectation
42
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Estimating E[Y] given moments for X|Y=0, X|Y>0, and X

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#probability-distributions #conditional-probability #statistical-inference #conditional-expectation #bayesian
208
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How to compute conditional expectation in Markov Chain?

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#markov-chains #conditional-expectation
52
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Random variable divided to its conditional expectation

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#probability #random-variables #expected-value #conditional-expectation
38
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If $\mathbb{E}( Y|Z=z)=0 $, then $\mathbb{E}(X Y|Z=z)=0 $

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#random-variables #expected-value #conditional-expectation
35
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Counterintuitive result on conditional expectation

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#random-variables #expected-value #conditional-expectation
48
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Relation between conditional expectation and CDF

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#probability #probability-distributions #expected-value #conditional-expectation
485
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$E(Cx+Dy | Ax+By=u)$

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#probability #conditional-expectation
48
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Given a $\sigma$-subalgebra $\mathcal{G}$, does there exist $X$ such that $\sigma(X) = \mathcal{G}$?

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#probability-theory #conditional-expectation
48
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Question on conditional expectation $E[(U_{t \wedge (s\vee \tau)} - U_{t\wedge \tau})X_{t \wedge \tau}|\mathscr{F}_s]=(U_s-U_{s\wedge \tau})X_\tau?$

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#probability #probability-theory #stochastic-processes #conditional-expectation #martingales
113
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Minimizing $E(|Y-f(X)|)$.

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#probability-theory #conditional-expectation #median
70
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On expected waiting time and distribution of departure times in M/M/1 queue, condition on the number of departures

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#stochastic-processes #expected-value #conditional-expectation #operations-research #queueing-theory
53
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Integral of conditional expectation over an event B

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#random-variables #lebesgue-integral #conditional-expectation
293
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Conditional variance of Y given X when y is a continuous function of x

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#statistics #expected-value #conditional-expectation #variance
31
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About conditional expectations

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#probability #expected-value #conditional-probability #conditional-expectation

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