Natural estimators

The random variables Xi are i.i.d. and satisfy E[X2i]=θ. Use a natural estimator to calculate an estimate of θ based on the values X1=1, X2=3, X3=−1, X4=2, X5=0.
unanswered

In order to calculate confidence intervals around your estimator, you need information on the variance of your estimator. This variance is determined by E[X2i] and E[Xai] for some other power a. What is the value of a?

a=
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If you do not have any prior knowledge about the value of E[Xai], can you estimate it based on the available data?
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2 answers

(a) 3
(b) unanswered
(c) Yes
(b) a = 4