Estimation Methods in Probability and Statistics

This lecture covers estimation methods in probability and statistics, focusing on maximum likelihood estimation. The instructor begins by reviewing previous topics, including the calculation of estimators for mean and variance. The lecture introduces the concept of likelihood functions and their significance in estimating parameters. The instructor explains how to derive the maximum likelihood estimator (MLE) and provides examples, including the exponential distribution. The discussion extends to the properties of estimators, such as bias and variance, and how they affect the quality of estimates. The lecture also addresses the construction of confidence intervals, detailing the methods for both known and unknown variance scenarios. The instructor emphasizes the importance of understanding the underlying statistical principles and the practical application of these estimation techniques. Throughout the lecture, various examples and visual aids are used to illustrate the concepts, ensuring clarity and comprehension for the audience.