Review of elementary probability, Formal definition of a probability space, axioms, examples, properties, Conditional Probability, Independence and conditional independence, independence of more than two events, Partition formula, Discrete random variables, definition, examples - Bernoulli, Binomial, Poisson, Uniform and Geometric random variables, distributions and properties, Expectation of a random variable, mean, variance, moments examples -Review of elementary probability, Formal definition of a probability space, axioms, examples, properties, Conditional Probability, Independence and conditional independence, independence of more than two events, Partition formula, Discrete random variables, definition, examples - Bernoulli, Binomial, Poisson, Uniform and Geometric random variables, distributions and properties, Expectation of a random variable, mean, variance, moments examples - Bernoulli, Binomial, Poisson, Uniform and Geometric Random Variables, Continuous Random Variable, definition probability distribution function - Uniform, Exponential, Gaussian Random variables, Mean and Variance, moments, moment generating functions, Joint distribution of random variables, Conditioning of random variables, conditioning on events, other random variables, conditional distributions, examples, Random vectors, multi dimensional probability distribution, moments, mean vector, covariance matrix, Random sequences, Bernoulli process, properties, Time of Kth arrival, Merging and splitting of Bernoulli processes, examples, Poisson Process, Definition, Applications, Number of Arrivals and Poisson PMF, Mean and Variance, Time of Kth Arrival, examples, Sum of independent poisson random variables, Merging/Splitting a Poisson process, Different sampling methods, Poisson versus normal approximations, Introduction to Markov Processes, Discrete time finite state Markov chains, N step transition probabilities, Markov Process - Recurrent and Transient states, steady state probabilities, Birth-death processes.