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Competitive Stats
Q4Section I (Objective (Q1–Q80))4 of 79

Distribution Theory — mean of a log-transformed uniform sum

Let X1,X2,X3,…,XnX_1, X_2, X_3, …, X_n be iid U(0,1)U(0,1) variates and T=−ln⁡(X1X2X3…Xn)T = -\ln(X_1X_2X_3… X_n). What is E(T)E(T) equal to?

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