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Q22Section A (Section A)22 of 60

Expectation of log uniform ratio

Let X1,X2X_1, X_2 and X3X_3 be three independent and identically distributed random variables having U(0,1)U(0, 1) distribution. Then E[(ln⁡X1ln⁡(X1X2X3))2]E\left[\left(\frac{\ln X_1}{\ln(X_1 X_2 X_3)}\right)^2\right] equals

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