Maximum Likelihood Estimation (MLE)

http://en.wikipedia.org/wiki/Maximum_likelihood

What is known
-The population distribution is parameterized (e.g. normal, binomial, ...)
-A bunch of samples is collected

Goal
Estimate the population distribution parameter

Recipe
See what parameter will have the greatest probability of producing these samples

Example
An unfair coin has head probability of either P = 0.3 or 0.8. It is flipped 100 times and turns up 43 heads. Find the MLE for P.