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Q9Section A (Section A)9 of 60

Limit in probability of the mean of squared normals

Let X1,X2,…X_1,X_2,… be a sequence of i.i.d. N(0,1)N(0,1) random variables. Then, as n→∞n\to\infty, 1n∑i=1nXi2\frac1n\sum_{i=1}^nX_i^2 converges in probability to

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