A sample of size 1 is drawn from the unifrom pdf defined over the interval . Find an unbiased estimator for .
Any help would be great. Thanks.
If your sample is , the unbiased estimate of . So a guess for the unbiased estimate of would be .
Recall that where is the probability density function, in this case . Therefore,
But if we want the estimator to be unbiased, we should have
Therefore, we see that our initial guess should be modified to be
This is the unbiased estimator of .
In general this is a trick you can use to find an unbiased estimator. Make a good guess that will make , then take .