Assume n independent observations, denoted Xi,
(i=1,....n), are taken from a distribution with a mean of...
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Assume n independent observations, denoted Xi,(i=1,....n), are taken from a distribution with a mean of E(X)=?and variance V(X) =?2. Prove that the mean of the n observationshas an expected value of E(X)=? and a variance of V(X) =?2/n. Usethe appropriate E and V rules in your answer. What happens as nbecomes large? What does this tell you about the quality of thesample mean as an estimate of ? as the sample sizeincreases?
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We have Consider Hence Similarly HenceWe observe
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