Expectation of −2 ln U

Let UU be Uniform(0,1)(0,1) and Y=−2ln⁡UY=-2\ln U. What is E[Y]E[Y]?

Show hints (2)+
  1. −ln⁡U∼Exp(1)-\ln U\sim\text{Exp}(1).
  2. Scaling an exponential scales its mean.

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