CSE 221: Probabilistic Analysis of Computer SystemsExampleExample (contd..)Slide 4Probability axiomsProbability axioms (contd..)Probability axioms: ExampleSlide 8Formulating a probability modelCombinatorial problemsCombinatorial problems: ExampleSlide 12CSE 221: Probabilistic Analysis of Computer SystemsTopics covered:Event algebra Probability axiomsCombinatorial problems(Sec. 1.5-1.8.1)ExampleSequence of three coin tosses:Event E1 – at least two headsComplement of event E1 – at most one head (zero or one head)Event E2 – at most two headsExample (contd..)Event E3 – Intersection of events E1 and E2. Event E4 – First coin toss is a headEvent E5 – Union of events E1 and E4Mutually exclusive eventsExample (contd..)Collectively exhaustive events:Defining each sample point to be an eventProbability axiomsSample space:Events:Assign probabilities to events:Example: A single coin tossProbability axioms (contd..)Probability axioms: ExampleSequence of three coin tossesCompute the probability of event E1 – at least one head. Compute the probability of event E2 – at most two heads.Probability axioms: ExampleSystem composed of CPU and memorySample space:Events of interest – System up & system down:Compute p(system up) and p(system down):Formulating a probability modelCombinatorial problemsOrdered sample of size k with replacementCombinatorial problems: ExampleOrdered sample of size k with replacement (example)Combinatorial problems: ExampleOrdered sample of size k with replacement
View Full Document
Unlocking...