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• Finite probability spaces: Basic concept
• probability and related frequency
• combination of events, examples
• independence, random variables
• expected value, standard deviation
• Chebyshev's inequality, independence of random variables
• multiplicatively of the expected value
• additivity of the variance, discrete probability distribution
• Probability as a continuous set function: Sigma-algebras, examples
• Mid Term Exam
• continuous random variables, expectation and variance
• normal random variables
• continuous probability distribution
• Applications: De Moivre-Laplace limit theorem
• weak and strong law of large numbers
• the central limit theorem
• Winter vacations Markov chains continuous Markov process
• Final Term Exam