Given the facts(adsbygoogle = window.adsbygoogle || []).push({});

1. [tex] X_1 ,...,X_n [/tex] are independent and have the same distribution.

2. The expectation value of [tex]X_i[/tex] is [tex] E\left( {X_i } \right) = \theta [/tex].

3. [tex]T=\sum\limits_{i = 1}^n {X_i }[/tex] is a sufficient statistic.

I'm asked to find an astimate for [tex]\theta[/tex] starting with the estimate [tex]U=X_1[/tex].

According to Rao-Blackwells theorem, the new estimate is taken as [tex]g(t)=E(U|T=t)[/tex].

I don't know how to calculate this expression further. Any help or tip would be appreciated.

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# Rao-Blackwells theorem

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