In: Statistics and Probability
I have a coin and I know that the probability p of flipping heads is either 1/2 or 1/4. I flip the coin 3 times and I get THT. Use the maximum likelihood method to determine the actual value of p.
note that the values of P(sample given p) is same as likelihood of p given an observed sample, the only difference being that former is a function of sample, and latter the function of p. The value of p that maximizes the likelihood , or equivalently, the probability of observed sample, is the mle. Please upvote if the solution is helpful for you.