APM_2F010_EP - Probability and Statistics (2024-2025)

MAA210 provides with an introduction to the beasic concepts of probability and statistics. The course covers the following topics

• Discrete probability spaces: independence and conditional probability
•  Discrete random variables: independence, joint distribution and marginal distribution.
• Expectation and variance of a discrete random variable: applications to binomial random variables, Poisson random variables and geometric random variables.
• Basic inequalities: Jensen, Markov and Chebyshev.
• Absolutely continuous random variables: Gaussian random variables, uniform random variables and exponential random variables
• Cumulative distribution function
• Expectation of an absolutely continuous random variable
• Quadratic convergence of random variables and law of large numbers for square integrable random variables
• Introduction to descriptive Statistics: of one and two-dimensional descriptive statistics (correlation and LS regression line)
• Random variables: variance, moment generating function, characteristic functions
• Convergence of a sequence of random variables and central limit theorem
• Introduction to parametric estimation: Estimation of the expectation, Maximum likelihood estimation
• Confidence interval and introduction to statistical tests: Confidence intervals, parametric tests