Maximum Likelihood Example: Bernoulli
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Googling "maximum likelihood binomial" will give you several direct analytical descriptions of this. Alternatively, you can think of a binomial rv as the sum of n Bernoulli rv's. So, N trials of a binomial is essentially n*N trials of a Bernoulli, and the argument given in this video applies.
The harder problem is ML binomial estimation when neither n nor p is known. I have not seen how to come up with the estimator analytically. Thankfully, n would usually be known in applications.
MathHolt 11 months ago