Let { X_i }_{i=1}^n be a sequence of independent draws from the Uniform distribution on (0,1) and le


Question: Let \[\left\{ {{X}_{i}} \right\}_{i=1}^{n}\] be a sequence of independent draws from the Uniform distribution on (0,1) and let \[{{Y}_{n}}=\sum\limits_{i=1}^{n}{{{X}_{i}}}\] .

a) Find E(Y) and Var(Y).

b) Find a function of Y that will be asymptotically standard Normal.

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