# compute the conditional expectation given by following random variables

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 $$\Bbb E(\xi|\eta):=\Bbb E(\xi|\sigma(x)).$$

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