Karteikarten
Probability Theory
Karten in diesem Stapel (22)
- 1Simple ExperimentSome well-defined act or process that leads to a single well-defined outcome.
- 2Sample SpaceThe set of all possible distinct outcomes (i.e., elementary events) for a simple experiment. Denoted with the symbol "S."
- 3Elementary EventSynonym: Sample point; Any member of the sample space.
- 4EventSynonym: Event Class; Any set of elementary events. A, B and so on represent subgroupings of elementary events that make up a sample space.
- 5A ∪ B∪ = Union; A ∪ B = A or B. In such a case, either A has occurred, B has occurred, or A and B have occurred.
- 6A ∩ B∩ = Intersection; A and B have occurred.
- 7∅The null event; empty set; the impossible event.
- 8~"Not;" Ex: ~A reads "not A." Therefore, the complement of event A is ~A.
- 9Mutually ExclusiveWhen two events cannot co-occur. For example, if A = alive and B = dead. In other words, if A (i.e., alive) is occurring, then B (i.e., dead) cannot be. A∩B=∅
- 10ExhaustiveA description for an event that means each elementary event in a sample space must qualify for one or more of the events within a sample space (i.e., A, B, or C).
- 11Family of EventsA group of all possible events than can occur in the sample space (i.e., S), including ∅ and S (i.e., \[2^N\]; N = discernibly different outcomes to the simple experiment)
- 12ProbabilitiesNumbers assigned to each and every event in a sample space.
- 13p(A)Probability of event A.
- 14p(∅)"Null" event or an impossible outcome in a simple experiment.
- 15Probability TheoryP(A) in a given S follows these axioms:
1. p(A) ≥ 0 for every event A.
2. p(S) = 1.00.
3. The probability of mutually exclusive events is the sum of their separate probabilities. - 16Probability Rule #1p(~A) = 1 - p(A)
The rule of complementary probability.
A U ~A = S - 17Probability Rule #20 ≤ p(A) ≤ 1.00 for any event A.
The probability range. - 18Probability Rule #3p(∅) = 0, for any S.
Rule of the impossible event. - 19Probability Rule #4For any two events A and B in S, p(A U B) = p(A) + p(B) - p(A ∩ B).
"Or" rule of probability. - 20Probability Rule #5If the set of events A, . . ., L constitutes a partition of S, then p(A U . . . U L) = p(A) + . . . + p(L) = 1.00.
In other words, when any two or more events are mutually exclusive and exhaustive and thus form a partition of S, the sum of their probabilities must be equal to 1.00. - 21Probability of Elementary Eventsp(A) = \[\frac{number of elementary events in A}{total number of elementary events in S}\] or p(A) = \[\frac{n(A)}{N}\].
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- Doctorate Mathematics Karteikarten am Probability Theory, erstellt von Kara Polk am 14/06/2017.
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- Kara Polk
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