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V. Conditional Probability. Stochastic Independence
Fichas del conjunto (6)
- 1P(A|H), where P(H) > 0P(A|H) = P(AH)/P(H)
- 2Law of total probabilitiesLet Hi be a set of mutually exclusive events of which one necessarily occurs. Let A be any event. Then:
P(A) = Sum [ P(A|Hi)*P(Hi) ] - 3Bayes's rule: P(Hk|A)P(Hk|A) = P(A|Hk)*P(Hk) / (Sum[P(A|Hi)*P(Hi)])
- 4Stocahstic independence of events A and HA and H are called stocahstically independent if:
P(AH) = P(A)*P(H) - 5Mutual independence if events A1, A2, ..., AnThe events A1, ..., An are called mutually independent it:
P(AiAj) = P(Ai)*P(Aj)
P(AiAjAk) = P(Ai)*P(Aj)*P(Ak)
...
P(A1A2...An) = P(A1)*P(A2)*...*P(An) - 6Combinatorial product of two sample spacesLet Q be a sample space consisting of events Xi with probabilities pi, and M be a sample space of events Yi with probabilities qi. Then G is a combinatorial product of Q and M if it consists of events (Xi, Yj) and P{(Xi, Yj)} = pi*qj
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- Probability Theory and It's Applications - W. Feller Fichas sobre V. Conditional Probability. Stochastic Independence, creado por Sergei Fomin el 22/08/2017.
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- Sergei Fomin
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