Unbiased Estimator

**jmat** · December 1st 2009, 05:02 AM

I have a question on unbiased estimators and im completely lost...
please help!

**statmajor** · December 1st 2009, 06:24 PM

What value of c would satisfy the following:

$E(c(X_1 + 2X_2)) = \frac{1}{\theta}$

**matheagle** · December 1st 2009, 09:02 PM

Originally Posted by statmajor

What value of c would satisfy the following:

$E(c(X_1 + 2X_2)) = \frac{1}{\theta}$

since they are i.i.d.

$3cE(X) = \frac{1}{\theta}$

**jmat** · December 2nd 2009, 12:34 AM

Originally Posted by matheagle

since they are i.i.d.

[tex]3cE(X) = \frac{1}{\theta}[/m
ath]

Sorry but can you explain what you just did? And what is I.I.d?

**mr fantastic** · December 2nd 2009, 12:51 AM

Originally Posted by jmat

Sorry but can you explain what you just did? And what is I.I.d?

It means independent and identically distributed. From which it follows that E(X1) = E(X2). From which matheagle's equation follows. And you should know how to calculate an expected value when you have the pdf.

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