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Lecture 2 Experiments, Models, & Probabilities

Dive into probability axioms, consequences, and applications in this lecture. Understand set theory, conditional probability, and independence. Learn through examples and theorems. Reading assignments included. Join us for an insightful session!

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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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