CSE 3504: Probabilistic Analysis of Computer Systems Topics covered: Conditional probability Independent events Bayes rule Bernoulli trials (Sec. 1.9-1.10)

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

Conditional probability (contd..) Example:

Independent events Definition: Mutually independent events: Pairwise independent events:

Independent events (contd..) Example:

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

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

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

Reliability of parallel systems: Example

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

Reliability of series/parallel systems: Example

Bayes rule Definition: Intuition:

Bayes rule: Example Sequence of three coin tosses:

Bayes rule: Example (contd..)

Bayes rule: Example Chip testing:

Bernoulli trials

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