The coin example. Assume that we have two coins, coin A and coin B(for short, A and B). There exist two different possibility distributions of A and B about whether heads or tails come down. We have no idea about the frequency about selecting A and B as well. We only know about the the results of tossing coins. To approximate this process, we assume out the possibility distribution of A and B and initialize them randomly. Then we use them to approximate the probability of selecting A or B for the coin used in the game. It's the expectation step. Then we approximate new probability distributions of A and B according to the probability of selecting coins based on maximum likelihood principle. It's the maximization step. We repeatedly do these two steps until one of them converges.