Linearity of Expectation: First Moment Method

This lecture covers the concept of Linearity of Expectation and introduces the First Moment Method, which is used to analyze random matrices and eigenvalues. The lecture also delves into indicator random variables and Buffon's Needle problem in probability theory, discussing the calculation of probabilities and lengths of needles. Furthermore, it explores transitive tournaments and Ham paths, providing insights into the minimum number of copies of a given structure in a graph. The instructor demonstrates how to force vectors to be orthogonal and discusses assignments that ensure orthogonality in vector spaces.