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Hi. I have random variables X and Y, where X is nominal and Y takes values of 0 and 1. I have n observations of the form , where several observations may share the same X. I denote (so p is a random variable which becomes determined when given X), and is an estimator for p. I want to know how good this estimator is - specifically, I want to approximately know Is there a standard way of doing this?
I think I have reduced the problem to that of estimating , in case this is any simpler. Thanks. -- Meni Rosenfeld (talk) 16:42, 6 September 2009 (UTC)
Actually I had an idea for this, but originally I thought it would be computationally intractable. After looking into it I see it's not that bad. The idea is to assume that p follows the beta distribution, find the MLE of the distribution parameters given the data, and calculate the mean and variance for those parameters. Does this sound reasonable? Is there a better way? -- Meni Rosenfeld (talk) 18:06, 6 September 2009 (UTC)
What are all the ring automorphisms of ? I believe Z has only one: the identity. What is the general procedure of approaching the problem of determining Aut(R)? Thanks.--Shahab (talk) 22:01, 6 September 2009 (UTC)