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Lecture 2 Experiments, Models, & Probabilities

This lecture covers probability axioms, consequences of the axioms, and applying set theory to probability. Topics include conditional probability, independence, and sequential experiments.

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Lecture 2 Experiments, Models, & Probabilities

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  1. Lecture 2 Experiments, Models, & Probabilities Last Time Motivation and Course Overview Set Theory Review Applying Set Theory to Probability Probability Axioms Some Consequences of the Axioms Reading Assignment: Sections 1.1-1.4 Probability & Stochastic Processes Yates & Goodman (2nd Edition) NTUEE SCC_02_2008

  2. Lecture 2: Axioms Today • Probability Axioms • Some Consequences of the Axioms Reading Assignment: Sections 1.1-1.4

  3. Lecture 1: Getting Started Next Week • Conditional Probability • Independence • Sequential Experiments Reading Assignment: Sections 1.4-1.7

  4. What have you learned about prob. and stats.? • Q1: Probability Space? • Q2: Tourists survey example

  5. Theorem A.1 :A, P( A ) = 1 - P( ) . Theorem A.2: If A  B, then P(B - A) = P(B ) = P(B) - P(A). Theorem 1.6: P(A  B) = P(A) + P(B) - P(AB)

  6. Let Sr = S P ( Ai1 Ai2 ...  Air) 1 < i1 < i2 < .. < ir < n Then P ( A1  A2 ...  An ) n = S Sr r=1 Theorem A.4 :P(A) = P(AB) + P(ABc)

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