Question: 3. (Limit theorems) Let U1, ..., Un be independent random variables having the follow- ing common pdf: f (20 ) = 1 - a ,

3. (Limit theorems) Let U1, ..., Un be independent random variables

3. (Limit theorems) Let U1, ..., Un be independent random variables having the follow- ing common pdf: f (20 ) = 1 - a , 20 1. a) What is the limit in distribution, as n -> co, of the following sequence of random variables Ult . . . + Un Vn = VUR + ... +Um b) What is the limit in distribution of the sequence of random variables V2 ? Explain your answers

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