A discrete random variable is a type of random variable that can take on a countable set of distinct values. Common examples include the number of children in a family, the outcome of rolling a die, ...

Random events and random variables differ from deterministic events and variables in that it is impossible to precisely predict their occurrences or numerical values. Before tackling the notion of ...

The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications. The world is also full of data. Probabilistic modeling and the related field of statistical ...

The total area under the curve must equal 1, representing the fact that the probability of some outcome occurring within the entire range is certain. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

The main property of a discrete joint probability distribution can be stated as the sum of all non-zero probabilities is 1. The next line shows this as a formula. The marginal distribution of X can be ...

ABSTRACT: This methodological article aims to present the type I Pareto distribution in a clear and illustrative manner for better understanding among social researchers. It also provides R scripts ...

ABSTRACT: One of the most important challenges in the design of the foundation of the Earth layer below the surface, the Summit Foundation, which can be a very large impact on the sustainability and ...

John von Neumann's spectral theorem for self-adjoint operators is a cornerstone of quantum mechanics. Among other things, it also provides a connection between expectation values of self-adjoint ...