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Q53Section C (Section C)53 of 60

Limit of a sum of uniforms with an n to the three quarters threshold

Let X1,…,XnX_1,…,X_n be independent and identically distributed random variables with U(0,1)U(0,1) distribution. Then lim⁡n→∞P(∑i=1nXi≤n2+n3/4)=\lim_{n\to\infty}P\left(\sum_{i=1}^nX_i\le\frac n2+n^{3/4}\right)= ___________.

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