A mathematical introduction to univariate probability theory with some applications, particularly to statistics. Topics will include the basic rules of probability, conditional probability, independent events, the Law of total probability, Bayes’ Theorem, univariate random variables, discrete and continuous distributions and the density function, expectation, variance, higher moments, and special discrete and continuous distributions such as Bernoulli, binomial, Poisson, uniform, exponential, gamma and normal.
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