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 }