Global Certificate in Probability Theory Basics
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⢠Probability Basics: Introduction to probability theory, sample spaces, events, and probabilities.
⢠Probability Axioms: Study of probability axioms, their interpretations, and consequences.
⢠Conditional Probability: Definition and properties of conditional probability, conditional independence.
⢠Discrete Random Variables: Concept of random variables, probability mass functions, cumulative distribution functions, and expectations.
⢠Continuous Random Variables: Concept of continuous random variables, probability density functions, cumulative distribution functions, and expectations.
⢠Joint and Marginal Distributions: Definition and properties of joint and marginal distributions, conditional distributions.
⢠Expected Values and Moments: Computation of expected values, variances, and higher moments for random variables.
⢠Common Random Variables: Study of common discrete and continuous random variables, their distributions, and properties.
⢠Theorem of Total Probability and Bayes' Rule: Derivation and applications of the theorem of total probability and Bayes' rule.
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