1. CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Conditional probability Independent events Bayes rule Bernoulli trials (Sec. 1.9-1.10)

2. Conditional probability  Assigning probabilities to events:  How does the probability of an event change, given that some information is available about another event.

3. Conditional probability (contd..)  Example:

4. Independent events  Definition:  Mutually independent events:  Pairwise independent events:

5. Independent events (contd..)  Example:

6. Reliability of a series system  Description of a series system:  Reliability of a component:  Reliability of a series system:

7. Reliability of a series system (contd..)  Example:

8. Reliability of parallel systems  Definition: only one component is expected to be functioning.

9. Reliability of parallel systems: Example

10. Reliability of series/parallel systems  Components can be arranged in a combination of series/parallel structures.

11. Reliability of series/parallel systems: Example

12. Bayes rule  Definition:  Intuition:

13. Bayes rule: Example  Sequence of three coin tosses:

14. Bayes rule: Example (contd..)

15. Bayes rule: Example  Chip testing:

16. Bernoulli trials

17. Bernoulli trials: Example  Sequence of three coin tosses:  What is the probability of 2 heads?