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Mathematical Statistics: Course Outline (MAT 413)

Mathematical statistics is the application of mathematics to statistics, which was originally conceived as the science of the state. the collection and analysis of facts about a country: its economy, land, military, population, and so forth.

Course Contents

  • Interpretations of Probability, Experiments and events, Definition of probability, Finite sample spaces, Counting methods,
  • The probability of a union of events, Independent events,
  • Definition of conditional probability,
  • Bayes theorem. Random variables, discrete distributions and continuous distributions,
  • Probability function and probability density function,
  • The distribution function, Bivariate distributions, Marginal distributions, Conditional distributions, Multivariate distributions,
  • Functions of random variables, The expectation of a random variable, Properties of expectations,
  • Variance. Moments,
  • The mean and the median, Covariance and correlation,
  • Conditional expectation,
  • Moment Generating functions,
  • Probability distribution functions,
  • Binomial, Negative Binomial
  • Poisson, 
  • Normal Distribution.

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