unbiased estimator

**kuntah** · March 19th 2008, 01:22 PM

We have the test samples $X_{1},...,X_{n}$ from
$U(-\theta,\theta)$
with parameter $\theta$

Now show that $T = (3/n) (X^{2}_{1}+....+X^{2}_{n})$
is an unbiased estimator for $\theta^2$

My main problem is that I don't know which distribution this U stands for, is it the uniform distribution?

Can someone solve this plz

**CaptainBlack** · March 20th 2008, 03:20 AM

Originally Posted by kuntah

We have the test samples $X_{1},...,X_{n}$ from
$U(-\theta,\theta)$
with parameter $\theta$

Now show that $T = (3/n) (X^{2}_{1}+....+X^{2}_{n})$
is an unbiased estimator for $\theta^2$

My main problem is that I don't know which distribution this U stands for, is it the uniform distribution?

Can someone solve this plz

You need to show that:

$E(T) = \theta^2$

There are two ways of doing this both fairly easy. The first is to write out
the intgral and do it, the second is to remember that the expectation operator
is linear, so:

$E(T) = \frac{3}{n} ~\sum_{i=1}^n E(x_i^2)$

RonL

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