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Consider the probability space $([0,1],\mathcal B[0,1],\Lambda)$ where $\Lambda$ is Lebesgue measure. Let $\xi$ and $\eta$ be two random variable . For any set $A$, denote by $\Bbb I_{A}(x)$ the indicator function taking value $1$ if $x\in A$ and $0$ if $x\notin A$.
Suppose $\xi(x) = x^4$ and $\eta(x) = 1$ for all $x\in[0,1]$. Compute the conditional expectation $\Bbb E(\xi|\eta):=\Bbb E(\xi|\sigma(x)).$

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Hint: The $\sigma$-field generated by $\eta$ is the trivial one.

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