# Math Help - Unbiased Estimator

1. ## Unbiased Estimator

Could someone please help with the attached problem. Intuitively I would think that the answer is 1 but I don't know how to demonstrate it.
Thanks for your help.

2. Originally Posted by Connemara Pony
Could someone please help with the attached problem. Intuitively I would think that the answer is 1 but I don't know how to demonstrate it.
Thanks for your help.
An unbiased estimator is one with expected value equal to that which is being estimated.

$E(\hat{\theta})=E(X_1+X_2+aX_3)=\theta+\theta+a\th eta=(2+a)\theta$

So to make this an unbiased estimator we need $a=-1$

RonL