![]() But how would we implement the method in practice? Well, suppose we have a random sample \(X_1, X_2, \cdots, X_n\) for which the probability density (or mass) function of each \(X_i\) is \(f(x_i \theta)\). ![]() (So, do you see from where the name "maximum likelihood" comes?) So, that is, in a nutshell, the idea behind the method of maximum likelihood estimation. It seems reasonable that a good estimate of the unknown parameter \(\theta\) would be the value of \(\theta\) that maximizes the probability, errrr.
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