This lecture covers the concept of maximum likelihood estimation for density estimation problems, focusing on the Bernoulli model. It explains how to estimate parameters by maximizing the likelihood function, using the example of a coin toss game. The lecture also discusses the unreliability of tests, such as rapid COVID-19 tests, and how to experimentally estimate sensitivity and specificity. Additionally, it delves into modeling likelihoods and the Bayesian inference in the context of screening tests for diseases like cervical cancer.