Probability and Basic Statistics

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