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CSE 221: Probabilistic Analysis of Computer Systems

CSE 221: Probabilistic Analysis of Computer Systems. Topics covered: Probability axioms Combinatorial problems (Sec. 1.5-1.8.3). Probability axioms. Sample space: Events: Assign probabilities to events: Example: A single coin toss. Probability axioms (contd..).

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CSE 221: Probabilistic Analysis of Computer Systems

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  1. CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Probability axioms Combinatorial problems (Sec. 1.5-1.8.3)

  2. Probability axioms • Sample space: • Events: • Assign probabilities to events: • Example: A single coin toss

  3. Probability axioms (contd..)

  4. Probability axioms: Example • Sequence of three coin tosses • Compute the probability of event E1 – at least one head. • Compute the probability of event E2 – at most two heads.

  5. Probability axioms: Example • System composed of CPU and memory • Sample space: • Events of interest – System up & system down: • Compute p(system up) and p(system down):

  6. Formulating a probability model

  7. Combinatorial problems • Ordered sample of size k with replacement

  8. Combinatorial problems: Example • Ordered sample of size k with replacement (example)

  9. Combinatorial problems: Example • Ordered sample of size k with replacement (example)

  10. Combinatorial problems • Ordered sample of size k without replacement

  11. Combinatorial problems (contd..) • Example: Ordered sample of size k without replacement

  12. Combinatorial problems (contd..) • Example: Ordered sample of size k without replacement

  13. Combinatorial problems (contd..) • Unordered sample of size k, without replacement

  14. Combinatorial problems (contd..) • Example: Unordered sample of size k, without replacement

  15. Combinatorial problems (contd..) • Example: Unordered sample of size k, without replacement

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