The weak convergence of empirical distribution functions subject to random perturbations and scale factors to a Gaussian process is established. This result is used to study the efficiencies of tests ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

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 ...

Forecasting for any small business involves guesswork. You know your business and its past performance, but you may not be comfortable predicting the future. Using Excel is a great way to perform what ...

Secret communication over public channels is one of the central pillars of a modern information society. Using quantum key distribution this is achieved without relying on the hardness of mathematical ...