Transcription of Review of Basic Probability Theory
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Review of Basic Probability Theory
LECTURE 2. Review of Basic Probability Theory Probability SPACE AND AXIOMS. Probability Theory provides a set of mathematical rules to assign probabilities to outcomes of random experiments, , coin flips, packet arrivals, stock prices, neural spikes, noise voltages, and so on. Given a random experiment, its sample space is the set of all out- comes. An event is a subset of the sample space and we say that an event A occurs if the outcome of the random experiment is an element of A. Let F be a set of events. A. Probability measure P : F [0, 1] is a function that assigns probabilities to the events in F . We refer to the triple ( , F , P) as the Probability space of the random experiment.
4 Review of Basic Probability Theory set of events is typically taken to contain all open subintervals of Ω, i.e., all intervals of theform (a,b), a,b∈ Ω. More formally, let Fbe thesmallest σ-algebra thatcontains all opensubintervalsin Ω. is σ-albegra is commonly referred to as the Borelσ-algebraB
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