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5 Suppose X1Xn are iid random variables with mean EX.pdf

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5. Suppose X1,,Xn are i.i.d random variables with mean E(X)= and variance VAR(X)=2. Sample variance is defined as Vn=n1i=1n(XiMn)2,1 where Mn is the sample mean. Show that the expected value of Vn is given by: E[Vn]=nn12 Hint: Manipulate Vn into the form: Vn=n1i=1n(Xi)2( Mn)2 Provide an explanation as to why the sample variance is not an unbiased estimator; in other words, why do we have the factor nn1 ?.

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5. Suppose X1,,Xn are i.i.d random variables with mean E(X)= and variance VAR(X)=2. Sample variance is defined as Vn=n1i=1n(XiMn)2,1 where Mn is the sample mean. Show that the expected value of Vn is given by: E[Vn]=nn12 Hint: Manipulate Vn into the form: Vn=n1i=1n(Xi)2( Mn)2 Provide an explanation as to why the sample variance is not an unbiased estimator; in other words, why do we have the factor nn1 ?

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5 Suppose X1Xn are iid random variables with mean EX.pdf

  • 1. 5. Suppose X1,,Xn are i.i.d random variables with mean E(X)= and variance VAR(X)=2. Sample variance is defined as Vn=n1i=1n(XiMn)2,1 where Mn is the sample mean. Show that the expected value of Vn is given by: E[Vn]=nn12 Hint: Manipulate Vn into the form: Vn=n1i=1n(Xi)2( Mn)2 Provide an explanation as to why the sample variance is not an unbiased estimator; in other words, why do we have the factor nn1 ?