So in a binomial distribution, we know that p^ = X / n is an unbiased estomator for p. Which means that when n approaces infinity, p^ approaches p. But how can I prove this mathematically? Any help would be appreciated!
So in a binomial distribution, we know that p^ = X / n is an unbiased estomator for p. Which means that when n approaces infinity, p^ approaches p. But how can I prove this mathematically? Any help would be appreciated!
An estimator is unbiased if its expected value is equal to the parameter. The limit criteria you described means an estimator is consistent.
Yes of course, I wrote it a little unprecise. But intuitively it's easy to see that the expected value of p^ has to be equal to p. Since p, the probability, is defined as the mean of an unlimited population. I'm looking for a more formal proof though.