Convolution of Random Variables

This lecture covers the concept of convolution of random variables, starting with the distribution of sums of independent random variables in both discrete and continuous contexts. The instructor explains the importance of symmetry properties and group structures in obtaining nice formulas. The lecture then delves into the computation of probabilities and cumulative distribution functions for the sum of random variables, showcasing the similarities and differences between the discrete and continuous cases. Finally, the general case is discussed, where the convolution of independent random variables is defined abstractly. The lecture concludes by emphasizing the versatility of convolution across different types of random variables.