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In the early development of probability theory, only discrete random variables (although not called random variables at the time) were considered. Isaac Newton (1643-1727) considered the idea of ...

Brazilian Journal of Probability and Statistics, Vol. 35, No. 3 (2021), pp. 435-441 (7 pages) The aim of this note is to give an elegant proof of a result due to E. G. Olds which concerns the density ...

The binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. The chi-square distribution is often used in ...

Abstract: In this chapter, we introduce the concept of a random variable and develop the procedures for characterizing random variables, including the cumulative distribution function, as well as the ...

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 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 ...

The hazard produced by natural phenomena on infrastructure and urban populations has been widely studied in the last 50 years. Researchers have recognised that the real danger posed by these phenomena ...