Titlebook: Introduction to Probability, Statistics & R; Foundations for Data Sujit K. Sahu Textbook 2024 The Editor(s) (if applicable) and The Author(

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Introduction to ProbabilityChapter .: The basic concepts of probability are introduced in this chapter. Elementary methods of counting, the number of permutations and the number of combinations are introduced and illustrated. Elementary methods for calculating probabilities are discussed and the general urn problem in probability is defined.

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Random Variables and Their Probability DistributionsChapter . defines the random variables and their probability distributions. Many properties such as mean, variance, and quantiles of random variables are also defined here. Laws for expectations and variances of linear functions of random variables are also discussed.

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Standard Discrete DistributionsChapter .: This chapter introduces the standard discrete distributions: Bernoulli, binomial, Poisson, geometric, hypergeometric and negative binomial. In each case the basic properties, such as mean and variance are obtained and the R commands to obtain probabilities and cumulative probabilities are illustrated.

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Standard Continuous DistributionsChapter .: This chapter introduces standard continuous distributions: exponential, normal, gamma and beta. As in Chap. ., here we find the means and variances and also discuss the R commands for finding various quantities for each distribution.

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Transformation and Transformed DistributionsChapter . is devoted to deriving distributions of transformed random variables in one and multiple dimensions. These techniques are used to derive sampling distributions of quantities of statistical interests while sampling from the normal distribution. Three new distributions: chi-squared, t and F are derived and their properties are discussed.

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Sujit K. Sahun aspects for smart cards and standards.- Key management.- Multiparty computations like voting schemes.- Public key cryptography.- Quantum cryptography.- Secret sharing schemes.- Sequences.- Web security...The

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