Let X 1 , , X n be i i d normal random variables with mean Icirc frac14 and standard deviation Iuml Recall that X Igrave (X 1 middot middot middot X n ) n is the sample average Let Show that E S Iuml 2 In statistics, S is called the sample variance E(X X) 1 i 1

Question: Let X 1 , . . . , X n be i.i.d. normal random variables with mean Î¼ and standard deviation Ï. Recall that XÌ

Let X₁, . . . , X_nbe i.i.d. normal random variables with mean Î¼ and standard deviation Ïƒ. Recall that XÌ… = (X₁+ · · · + X_n)/n is the sample average. Let

-E(X; - X)². п — 1 i=1

Show that E[S] = Ïƒ². In statistics, S is called the sample variance.

-E(X; - X). 1 i=1

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