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Applied Probability Lecture 4

Applied Probability Lecture 4. Tina Kapur tkapur@ai.mit.edu. Objective. Use Probability to create a software solution to a real-world problem. Objective. Use Probability to create a software solution to a real-world problem. Timeline/Administrivia. Friday: vocabulary, Matlab

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Applied Probability Lecture 4

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  1. Applied Probability Lecture 4 Tina Kapur tkapur@ai.mit.edu

  2. Objective Use Probability to create a software solution to a real-world problem.

  3. Objective Use Probability to create a software solution to a real-world problem.

  4. Timeline/Administrivia • Friday: vocabulary, Matlab • Monday: start medical segmentation project • Tuesday: complete project • Wednesday: 10am exam • Lecture: 10am-11am, Lab: 11am-12:30pm • Homework (matlab programs): • PS 4: due 10am Monday • PS 5: due 12:30pm Tuesday

  5. Vocabulary • Random variable • Discrete vs. continuous random variable • PDF • Uniform PDF • Gaussian PDF • Bayes rule / Conditional probability • Marginal Probability

  6. Random Variable

  7. Random Variable • Function defined on the domain of an experiment

  8. Example r.v. • Experiment: 2 coin tosses • Sample space: • Random variable:

  9. Example r.v. • Experiment: 2 coin tosses • Sample space: HH, HT, TT, TH • Random variable: h number of heads in run

  10. Discrete vs. Continuous R. V.

  11. Discrete vs. Continuous R. V. • Domain

  12. PDF

  13. PDF • Function that associates probability values with events in sample space.

  14. PDF • Function that associates probability values with events in sample space. • Two characteristics of a PDF:

  15. PDF • Function that associates probability values with events in sample space. • Two characteristics of a PDF: • Mean or Expected value • Variance

  16. Uniform PDF

  17. Uniform PDF p(x) E(x) = s2(x) = ? 0 a x

  18. Gaussian PDF

  19. Gaussian PDF

  20. Bayes Rule Revisited

  21. Recitation/Lab • Install Matlab • Start Problem Set 1

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