Question: Let X 1 , X 2 , ... be a sequence of i.i.d. random variables with expected value and standard deviation . The samplestandarddeviation of

Let X1,X2,... be a sequence of i.i.d. random variables with expected value and standard deviation . The samplestandarddeviation of X1,...,Xn is defined as

sn=n11i=1n(XiXn)2 ,

where Xn=n1i=1nXi is the samplemean. Prove that sn in probability.

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