STATISTICS: Find a function of Y-bar that is an un-biased estimator of theta. In general how do you do this?

These are not questions I have to turn in, but I don't understand how to find un-biased estimator functions among other things... Any ideas on any of this would be very greatly appreciated.





For example, the reading on a voltage meter connected to a test circuit is uniformly distributed over the interval (theta, theta + 1) Where theta is the true but unknown voltage of the circuit. Suppose that Y(1), Y(2), ....... , Y(n) denote a random sample of such readings.





a. Show that Y-Bar is a biased estimator of theta and compute the bias.





b. Find a function of Y-bar that is an unbiased estimator of theta





Another one that is driving me mad, (I can't find similar done examples), is:





Let Y(1), Y(2), ...... , denote a random sample of size n from a population whose density is given by:





f(y) = ay^(a-1) /theta^a 0%26lt;= y %26lt;= theta, and 0 elsewhere.





"a" is a known fixed value but theta is unknown. Now consider the estimator theta-hat = max(Y(1), Y(2) ...... Y(n)).





a. Show that theta-hat is a biased estimator for theta.





What I also could really use is some sort of PDF/webpage that has examples of how to do these, I can't seem to find good ones.





Thanks for any help you might have.





Brian|||use the Pearson's chi square test