Question: Let U1,U2,,Un be independent and identically distributed random variables from Uniform(0,1). (a) Derive the probability density function of X1=logU1. Which family of distributions does it

Let U1,U2,,Un be independent and identically distributed random variables from Uniform(0,1).

Let U1,U2,,Un be independent and identically distributed random variables from Uniform(0,1). (a) Derive the probability density function of X1=logU1. Which family of distributions does it belong to? [5 marks] (b) Use the result in part (a), or otherwise, to show that the moment generating function of Y=log(U1U2Un) is MY(t)=(1t)n1,t

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