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Trying to solve the task from above, I'm having trouble with solving the last part. My idea was to find both $E[-Y_1]$ and $E[\frac{Y_n}{2}]$ and show, that both are equal to $\frac{n}{n+1}\theta$. The answers provided by the book say, that $\frac{n+1}{n} \hat\theta$ is the MVUE of $\theta$.
My calculations lead me to completely another answer, I'm wondering if there is a typo in the book, or if my calculations are bad. Tried to find mistake, but couldn't. Or maybe the method is completely wrong for some reason, that I don't see?

For those brave enough, to go through my calculations, here they are.

Thanks in advance for all Your help.

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fulaphex
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1 Answers1

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For anybody, that would have simmilar problem. You need to get the distribution of $\hat\theta$ and then get expected value based on that.

fulaphex
  • 115