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Q58Section C (Section C)58 of 60

Conditional mean on the left half

Let XX be a random variable with probability density function f(x)={3x2if 0<x<1, 0otherwise.f(x)=\begin{cases}3x^2& \text{if }0<x<1,\ 0& \text{otherwise.}\end{cases} Let δ\delta denote the conditional expectation of XX given that X≤12X\le\frac12. Then the value of 80δ80\delta is equal to __________ (answer in integer)

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