Combinatorics 03 Measure

Please find linked:

• Som Phene . Prakhar Patel - SoS IIT Bombay India - Combinatorics 01-03 I
• May 22, 2021 06:15 AM Eastern Time (US and Canada) Som Phene . Prakhar Patel - Meeting Recording - Counting 03
• 2021.05.22 Som Phene . Prof. Tasho Kaletha . Prof. Jinho Baik - Dept. of Mathematics, University of Michigan, Ann Arbor - Probability Kolmogorov Axioms 0I

Probability

• Experiment
  • Coin Flip
  • Die Roll
  • Urn ball draw
  • Draw number between 0 and 1
• Kolmogorov Axiom: Experiment Model is Probability Space.
  • Probabibility Space \((\Omega, \mathcal{F}, P )\)
  • Sample Space \(\Omega\), Outcome Set
  • Event Space \(\mathcal{F}\), \(\sigma\)-Algebra
  • Probabilty measure \(P \colon \mathcal{F} \to [0-1]\).
• Experiment - Kolmogorov Axiom - Model Probability Space
  • Coin Flip . Sample Space \(\Omega\), Outcome Set . \(\{H,T\}\)
  • Die Roll . Sample Space \(\Omega\), Outcome Set . \(\{1,2,3,4,5,6\}\)
  • Urn ball draw . Sample Space \(\Omega\), Outcome Set . as per condition
  • Draw number between 0 and 1
    • Sample Space \(\Omega\), Outcome Set . \([0-1]\)
    • Draw number between 0 and 1 . Sample Space \(\Omega\), Outcome Set . rational in \([0-1]\)
    • Draw number between 0 and 1 . Sample Space \(\Omega\), Outcome Set . finite list in \([0-1]\)
• Counting Axiom of Choice
  • 2019.08.02 Som Phene . Prof. Sanjoy Pushti - Dept. of Mathematics, IIT Bombay - Finite, Countable, Uncountable
  • 2012.02.05 Thomas Forester - Philosophy Department University of Auckland - Axiom of Choice and Inference to the Best Explanation

R

• Prakhar suggests Introduction to Probability Models by Sheldon Ross.