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Components of Probability Experiments • Elementary Outcome (ω) - an outcome of a random process. Examples 1. ω = T T T T H 2. ω = 3.527 seconds 3. ω = (router 1 down, router 2 down, recipient computer up) = DDU • Sample Space (Ω) - set of all possible outcomes. Examples 1. Toss coin until a head: Ω = {H, T H, T T H, T T T H, . . .} 2. Time to access webpage: Ω = (0, ∞) 3. Network Routers: Ω |Ω| = {ordered triples of U’s and D’s} = {DDD, DDU, DU D, U DD, U U D, U DU, DU U, U U U } = 8 = 23 - Discrete Sample Space - sample space with a finite our countably infinite number of elements. Examples 1. Toss coin until a head: Discrete (Countably infinite number of elements) 2. Time to access webpage: Not discrete 3. Network Routers: Discrete (Finite number of elements) - Note that there are usually multiple ways to express the sample space for a particular situation. Example 1. Toss coin until a head: Ω0 = {1, 2, 3, . . .} is an equivalent expression for the sample space. • Event (A) - A ⊂ Ω i.e., A is a subset of Ω (A collection of elementary outcomes). Examples 1. Toss coin until a head: A = = first head occurs between 5 and 11 tosses (inclusive) {5, 6, 7, 8, 9, 10, 11} 2. Time to access a webpage: B = More than 10 sectonds = (10, ∞) 3. Suppose the message is transmitted successfully if at least one router is up and the recipient’s computer is up. C = Successful transmission = {DDU, U DU, U U U }