A new proof, based on the duality theorem of linear programming, is given of a theorem of V. Strassen, which states essentially that the minimum distance between random variables with given ...
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 ...
Density functions are nonnegative for all real numbers but greater than zero only at a finite or countably infinite number of points. Density functions are nonnegative for all real numbers and are ...
The Annals of Mathematical Statistics, Vol. 43, No. 5 (Oct., 1972), pp. 1719-1726 (8 pages) Let {Xn, n ≥ 1} be a sequence of random variables such that for suitably ...
Chance and uncertainty play a role in many aspects of life. A solid understanding of probability enhances critical thinking and empowers us to make well-informed decisions in everyday situations such ...
The Virginia Lottery offers a game called the New Year's Millionaire Raffle for which the top prize is one million dollars. There are 375,000 tickets sold, of which 508 are winners. There are three ...
A courseware module that covers the fundamental concepts in probability theory and their implications in data science. Topics include probability, random variables, and Bayes' Theorem.
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