Question: please solve it on page by handwriting 3. (Limit theorems) Let U1, ...; Un be independent random variables having the follow- ing common pdf: f(I)

please solve it on page by handwriting

3. (Limit theorems) Let U1, ...; Un be independent random variables having the follow- ing common pdf: f(I) = 10 1- x , x 51, . = >1. a) What is the limit in distribution, as n -> co, of the following sequence of random variables V, = Uit .". + Un ? VUP + ...+ UR b) What is the limit in distribution of the sequence of random variables V2 ? Explain your answers

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