0. CSE 3504: Probabilistic Analysis of Computer Systems
Topics covered:
Conditional probability
Independent events
Bayes rule
Bernoulli trials
(Sec )

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

2. Conditional probability (contd..)
Example:

3. Independent events Definition: Mutually independent events:
Pairwise independent events:

4. Independent events (contd..)
Example:

5. Reliability of a series system
Description of a series system:
Reliability of a component:
Reliability of a series system:

6. Reliability of a series system (contd..)
Example:

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

8. Reliability of parallel systems: Example

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

10. Reliability of series/parallel systems: Example

11. Bayes rule
Definition:
Intuition:

12. Bayes rule: Example
Sequence of three coin tosses:

13. Bayes rule: Example (contd..)

14. Bayes rule: Example
Chip testing:

15. Bernoulli trials

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