Probability Distributions: Moments and Quantiles

This lecture covers the definition of moments for a distribution, including raw moments, centered moments, and factorial moments. It also explains the importance of expectation and variance in measuring the location and spread of a random variable. The lecture introduces the concept of conditional expectation and provides examples of calculating variances for Poisson and other distributions. Additionally, it discusses the classification of random variables into discrete, continuous, and mixed types, with examples like the exponential and Laplace distributions. The lecture concludes with the definition of quantiles and their significance in probability distributions.