$X,Y$ are both Continuous uniformly distributed.
What is the method to find $E(Y^2)$?
Any help is appreciated.
2026-04-07 04:51:25.1775537485
$X \sim U(0,1), Y \sim U(X,1)$, what is $E(Y^2)$
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As commented this is just a matter of using the Law of Total Expectation.
$\qquad\begin{align}\mathsf E(Y^2) & =\mathsf E(\mathsf E(Y^2\mid X))\\&=\int_\Bbb R\left(\int_\Bbb R y^2\,f_{Y\mid X}(y\mid x)\,\mathrm d y\right) f_{X}(x)\,\mathrm d x\\ &=\int_0^1\int_x^1\frac{y^2}{1-x}\,\mathrm d y\,\mathrm d x\\&~~\vdots\end{align}$