[問題] 統計問題

[AthrunZala ()]

有3題統計問題

請會的人可以提點一下

打的不是很好

請見諒

謝謝


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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推 jinndu:第一題在期望值中間+mean-mean再拆成兩組平方，就解出。