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Common Estimators † Sample mean (Y) Yi independent with mean „ and variance ¾2 E(1 n X Yi)= 1 n X E(Yi)=1 n n„ = „ Var(1 n X Yi)= 1 n 2 X Var(Yi)=1 n2 n¾2 = ¾2=n What is distribution of Y?. To Z and Y we obtain EE(ZjY)= E(Z) which is the same as EE(g(X)jY)= E(g(X)) 2 This property may seem to be more general statement than (i) in Theorem 1 The proof above shows that in fact these are equivalent statements 3 E(XYjY)=YE(XjY) Proof E(XYjY =y)=E(yXjY =y)=yE(XjY =y)(because y is a constant) Hence, E(XYjY)=. ï7 Ò‚î ÙÊ ¢„á Ÿªå‹ü©¹ `{ó;.

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