The first step is to ensure that the given distribution actually is a valid probability distribution. As mentioned earlier, this involves checking two key properties: non-negativity and summation to ...

Continuous Variable: can take on any value between two specified values. Obtained by measuring. Covariance: a measure of the direction of the linear relationship between two variables. Discrete ...

We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric ...

This is a graduate-level course focused on techniques and models in modern discrete probability. Topics include: the first and second moment methods, Chernoff bounds and large deviations, martingales, ...

This is a preview. Log in through your library . Abstract This paper studies a new class of Z-valued random variables, called beta unimodal, which are 'dot products' (in the sense of Steutel and van ...

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 ...

Text: A First Course in Probability by Sheldon Ross. Pearson, 9th ed, 2012, ISBN: 032179477X. Course goals: This course will develop the fundamental principles of probability as well as an ...

A random variable that can take only a certain specified set of individual possible values-for example, the positive integers 1, 2, 3, . . . For example, stock prices are discrete random variables, ...