[問題] 統計問題
有3題統計問題
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1.This exercise shows that the sample variance is an
unbiased estimator of the population variance
when Y1…..Yn ﹐are i.i.d with meanμ(y) and varianceσ^2 (y) .
_ 2 _ _
a. show that E[(Yi-Y)] = Var(Yi) +2cov(Yi,Y) +Var(Y)
_
b. show cov(Yi,Y )= σ^2 (y)/n
2 2
c. use the results in parts (a) and (b) to show E(S(y))= σ (y)
2.
Suppose that (Xi,Yi) are i.i.d with finite forth moments.
Prove that the sample covariance is a consist estimator
of the population covariance that is Sxy =σxy
3.
_ _
show that the pooled standard error {SE(pooled)[Y1-Y2]}
equals the stardend error for the difference in
means when the two group sizes are the same.
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10/29 15:25, , 1F
10/29 15:25, 1F
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