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CSE 3504: Probabilistic Analysis of Computer Systems

CSE 3504: Probabilistic Analysis of Computer Systems. Topics covered: Special discrete distributions Sec. 2.5.1.-2.5.4. Bernoulli pmf. What is a Bernoulli trial? Sample space: Bernoulli random variable:. Bernoulli pmf (contd..). pmf: Distribution function: Parameters:.

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CSE 3504: Probabilistic Analysis of Computer Systems

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  1. CSE 3504: Probabilistic Analysis of Computer Systems Topics covered: Special discrete distributions Sec. 2.5.1.-2.5.4

  2. Bernoulli pmf • What is a Bernoulli trial? • Sample space: • Bernoulli random variable:

  3. Bernoulli pmf (contd..) • pmf: • Distribution function: • Parameters:

  4. Bernoulli pmf (contd..) • Where to use: • Example: Tossing a biased coin.

  5. Binomial pmf • Relationship between Bernoulli and Binomial random variables: • Sample space: • Definition of Binomial random variable:

  6. Binomial pmf (contd..) • pmf: • Distribution function: • Parameters of a Binomial distribution:

  7. Binomial pmf (contd..) • Where to use: • Example: Sequence of three coin tosses:

  8. Geometric pmf • Relation between Bernoulli and Geometric pmf: • Sample space: • Definition of Geometric pmf:

  9. Geometric pmf (contd..) • pmf: • Distribution function: • Parameters of a Geometric distribution:

  10. Modified geometric pmf • Relation between Bernoulli pmf, geometric pmf and modified geometric pmf: • Sample space: • Definition of modified geometric pmf:

  11. Modified geometric pmf (contd..) • pmf: • Distribution function: • Parameters of a modified geometric distribution:

  12. Modified geometric pmf (contd..) • Where to use: • Example:

  13. Geometric distribution: Memoryless property • Definition:

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