# Unbiased Estimator

• Dec 1st 2009, 05:02 AM
jmat
Unbiased Estimator
I have a question on unbiased estimators and im completely lost...
• Dec 1st 2009, 06:24 PM
statmajor
What value of c would satisfy the following:

$\displaystyle E(c(X_1 + 2X_2)) = \frac{1}{\theta}$
• Dec 1st 2009, 09:02 PM
matheagle
Quote:

Originally Posted by statmajor
What value of c would satisfy the following:

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

since they are i.i.d.

$\displaystyle 3cE(X) = \frac{1}{\theta}$
• Dec 2nd 2009, 12:34 AM
jmat
Quote:

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?
• Dec 2nd 2009, 12:51 AM
mr fantastic
Quote:

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.