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Q49Section C (Section C)49 of 60

Expected sample minimum of a heavy-tailed density

Let X1,X2,X3X_1,X_2,X_3 be i.i.d. random variables from a continuous distribution having probability density function f(x)={12x3,if x>12, 0,if x≤12.f(x)=\begin{cases}\dfrac1{2x^3},&\text{if }x>\dfrac12,\ 0,&\text{if }x\le\dfrac12.\end{cases} Let X(1)=min⁡{X1,X2,X3}X_{(1)}=\min\{X_1,X_2,X_3\}. Then the value of 10E(X(1))10E(X_{(1)}) is equal to __________ (answer in integer)

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