Probability and Basic Statistics

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Course Outline

  • Random Experiments – Sample space - Events – Axioms of Probability.
  • The basic principle of counting and combinatorial analysis
  • Conditional Probability and Independence
  • Random variables – Cumulative distribution function and probability density function - Jointly Distributed Random Variables.
  • Expected value, Variance and Standard deviation.
  • Probabilistic inequalities (Markov, Chebyshev, Jensen).
  • Moment Generating Functions – Probability Generating functions
  • Distributions of Discrete Variables (Bernoulli, Binomial, Geometric, Poisson).
  • Distributions of Continuous Variables (Uniform, Normal, Exponential) - Poisson Process
  • Central Limit Theorems.
  • Descriptive statistics - Correlation of statistical data – Data transformations.
  • Inferential statistics - Point Estimation – Estimator Functions
  • Special random distributions (χ2, t, F) – Confidence Intervals for the Normal Mean, the Variance and the difference in Means of Two Normal Populations - generalization in Non-Normal Populations.
  • Linear Regression

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