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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Rao-Blackwells theorem

**Physics Forums | Science Articles, Homework Help, Discussion**