# Variance of Estimator / Variance Algebra

I think ive got this correct, but i keep second guessing myself. I have an estimator of an ordered statistic, assuming distributed Uniform[0, 1]

The estimator is defined as:

$$\hat \theta = X_{(1)} - \frac{1}{n+1}$$

Im solving for the variance of this estimator, is the following correct?

$$Var(\hat \theta) = Var(X_{(1)} - \frac{1}{n+1} )$$

Can that just be simplified to:

$$Var(\hat \theta) = Var(X_{(1)} )$$

ie just drop the 1 / (n+1) term as a constant - or can this not be considered a constant.

Thanks

• Sorry further information, the distribution is uniform between $[\theta and \theta + 1]$ ive used a transformation for calculating other variables ie E(theta) to make it uniform between 0 and 1 which is much easier. Just not sure about the variance – James May 22 '14 at 8:09

Well it depends on what $n$ is of course. It looks like a constant, in particular the size of your sample, in which case yes you can discard a constant when dealing with variance; a translation does not affect the 'spread'.