[See Solution] (2 mark) Let X_i _i=1^n be a sequence of independent draws from the Uniform distribution on (0,1) and let Y_n=∑limits_i=1^nX_i . Find E(

Question: (2 mark)

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

Find E( Y ) and Var( Y ).
Find a function of Y that will be asymptotically standard Normal.

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[See Solution] (2 mark) Let X_i _i=1^n be a sequence of independent draws from the Uniform distribution on (0,1) and let Y_n=∑limits_i=1^nX_i . Find E(

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