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Q16Section A (Section A)16 of 60

Expectation from a piecewise cumulative distribution function

Let XX be a random variable with the cumulative distribution function

F(x)={0,x<0, x8,0≤x<2, x216,2≤x<4, 1,x≥4.F(x)=\begin{cases}0, & x<0,\ \frac x8, & 0\le x<2,\ \frac{x^2}{16}, & 2\le x<4,\ 1, & x\ge4.\end{cases}

Then E(X)E(X) equals

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