Markov's inequality gives an upper bound on the probability that a nonnegative random variable takes large values. For example, if the random variable is the lifetime of a person or a machine, ...

This is a graduate-level course focused on techniques and models in modern discrete probability. Topics include: the first and second moment methods, martingales, concentration inequalities, branching ...

A recurrent theme of interest in probability and statistics is to determine the best bounds for two probabilities, Pr(X ≥ r) and Pr(s < X - μ < t), when only the mean μ and the standard deviation σ of ...