A divergent reciprocal expectation

XX is uniform on (0,1)(0,1). Does E[1/X]E[1/X] exist (finitely)?

Show hints (2)+
  1. Integrate 1/x over (0,1).
  2. ∫ 1/x dx near 0 behaves like ln x.

Answer

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No - it diverges to +∞+\infty

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