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This lecture covers the comparison of two simple hypotheses, Neyman-Pearson lemma, rejection regions, optimal tests, probabilities, likelihood, maximum likelihood estimation, observed and expected information, and the construction of confidence intervals. It also discusses the likelihood ratio statistic, limit distribution of the maximum likelihood estimator, and the elements of a statistical hypothesis test. The instructor explains the importance of p-values, power of tests, and decision-making based on statistical evidence.