6.01 Lecture Notes - Lecture 1: Joint Probability Distribution, Bayes Estimator, Probability Theory
13 Apr 2016
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Topics: probability, bayes" theorem, markov processes, bayesian inference. Probability theory provides a framework for modeling and reasoning about uncertainty making precise statements about uncertain situations and drawing reliable inferences from unreliable observations. Probability theory provides a framework for designing systems that are robust to uncertainty. Probabilities are assigned to events, which are possible outcomes of an experiment. There are eight atomic events: hhh, hht, hth, htt, thh, tht, tth, ttt. Set of all atomic events is collectively exhaustive (cover all cases) Set of all possible atomic events is called the sample space u. The probabilities that are assigned to events must obey three axioms: Non-negativity: pr(a) 0 for all events a. Additivity: if a b is empty, pr(a b) = pr(a) + pr(b) Example: assume the probability of rain on a given day is 0. 1. However, if it rains today, the probability of rain tomorrow is 0. 15.
