CSE 3504: Probabilistic Analysis of Computer Systems Topics covered: Probability axioms Combinatorial problems (Sec )

Probability axioms  Sample space:  Events:  Assign probabilities to events:  Example: A single coin toss

Probability axioms (contd..)

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.

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):

Formulating a probability model

Combinatorial problems  Ordered sample of size k with replacement

Combinatorial problems: Example  Ordered sample of size k with replacement (example)

Combinatorial problems: Example  Ordered sample of size k with replacement (example)

Combinatorial problems  Ordered sample of size k without replacement

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

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

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

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

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