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

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?