Applied Probability

This course provides a comprehensive introduction to applied probability and probability distributions. Students will learn probability with an understanding of its applications in statistical inference. Topics include discrete and continuous random variables and distributions, such as the binomial, negative binomial, Poisson, geometric, uniform, normal, exponential, gamma, beta, chi-square, t, and F. This course thoroughly develops topics as transformation of variables, joint distributions, bivariate normal, expectations, conditional distributions and expectations, moment-generating functions, distribution of sums of random variables, means and variances of sums, ratios of independent variables, and central limit theorem. Students will acquire an excellent background to proceed to statistical inference.