MA933 - Networks and Random Processes MSc in Mathematics of Systems
نویسنده
چکیده
Definition 1.1 A probability distribution P on (Ω,F) is a function P : F → [0, 1] which is (i) normalized, i.e. P[∅] = 0 and P[Ω] = 1 (ii) additive, i.e. P [ ∪i Ai ] = ∑ i P[Ai] , where A1,A2, . . . is a collection of disjoint events, i.e. Ai ∩ Aj = ∅ for all i, j. The triple (Ω,F ,P) is called a probability space. For discrete Ω: F = P(Ω) and P[A] = ∑ω∈A P[ω] e.g. P[even number on a die] = P[2] + P[4] + P[6] = 1/2 For continuous Ω (e.g. [0, 1]): F ( P(Ω)
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