Variance and Covariance: Properties and Examples

This lecture covers the definition of variance and covariance of random variables, including properties such as linearity and independence. It also explores examples involving Poisson and normal distributions, as well as the standard deviation. The instructor discusses the relationship between covariance and dependence, as well as correlation and linearity. Practical applications are illustrated through examples related to atmospheric ozone, soil acidity, and stork births. The lecture concludes with the law of large numbers and its application in analyzing the outcomes of repeated experiments.