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The expected value of a random variable is a weighted average of all possible values a random variable can take on, with the weights equal to the probability of taking on that value.
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Conditional expectation of (degenerate) trivariate normal?
Say $A$ and $B$ are both independent, normally distributed. $A\sim\mathcal{N}(\mu_{A},\sigma^{2}_{A})$ and $B\sim\mathcal{N}(0,\sigma^{2}_{B})$ define $C=A+B$. Then $(A,B,C)'$ are degenerate, joint tr …