Karteikarten
Probability
Karten in diesem Stapel (45)
- 1Classical defnumber of ways an event can occur/total number of possible outcomes (only if they are equally likely)
- 2Relative frequency defThe prob of an event is the proportion of times the event occurs in a very long series of repetitions of an experiment
- 3Subjective defThe prob of an event is a measure of how sure the person making the statement is
- 4ExperimentIs a process with multiple possibilities that can be repeated under the same conditions
- 5Trialone instance of an experiment
- 6Outcomepossible result on one trial of an experiment
- 7Sample spaceSet of all possible outcomes on one trial of an experiment
- 8Sample space properties- no repeated items (sample points)
- order does not matter
- nothing can be left out
- two types based on size (countable-discrete or uncountable-continuous) - 9EventIs a subset of the sample space S
- 10Event properties- could include empty set or S (everything)
- simple (one element) or compound (more elements)
- once an event occurs, we say the event A occurs iff the outcome is in the subset A - 11Addition ruleOR +
- 12Multiplication ruleAND
- 13ProbabiliyP is a function that maps event to real numbers such that
0 <= P(A) <= 1, for any event
P(S) = 1 - 14Impossible eventHas a probability 0
- 15Certain eventHas a probability 1
- 16Compound eventProbability is the sum of the probabilities of all the sample events inside it
- 17OddsThe odds in favour of an event A is the probability the event occurs divided by the probability
it does not occur or
P(A)/1-P(A) . The odds against the event is the reciprocal of this,
1-P(A)/P(A) . - 18P(A)number of outcomes in A/number of outcomes in S
- 19With replacementThe thing is replaced for the same one after first event
it is possible to select the same object more than once - 20Without replacementThe thing is not replaced, must subtract from total
once an object is selected, it is not possible to select it again - 21PermutationOrder matters
Without replacement
ways, sequences, arrangements
nPk, big permutation small - 22n!n factorial
arrangements of length n using each symbol once and only once - 23n^(k)n to k factors
arrangements of length k using each symbol at most once
n!/(n-k)! - 24n^karrangements of length k using each symbol as often as we wis
- 25ComplementA', is the set of all outcomes in S which are
not in A. - 26Solving permutationsWays, arrangements
if restrictions, place it first - 27CombinationsOrder doesn't matter
Without replacement
nCk, big choose small - 28Combination properties1. nC0 and nCn = 1
2. nCk = nC(n-k) choosing k is the same as excluding k
3. Pascal's identity - 29Arrangements where some objects are the samen!/n1! n2! n3!... nk!
where n above is how many object in total and n below how many for the specific type - 30A subset BIf A and B are two events with A subset B (that is, all of the points in A are also in B), then
P(A) <= P(B) - 31A ∪ Bunion, OR
- 32A ∩ Bintersection, AND
can be written as AB or just ABC - 33A'complement
everything that isn't A - 34De Morgan's Laws(A ∪ B)' = A' ∩ B'
(A ∩ B)' = A' ∪ B' - 35P (A ∪ B)P(A) + P(B) - P(AB)
or for three
P(A) + P(B) + P(C) - P(AB) - P(AC) - P(BC) + P (ABC)? - 36Mutually exclusiveP(AB) = 0
Cannot occur together - 37IndependentP(AB)=P(A)P(B)
Does not influent each other - 38ComplementP(A') = 1 - P(A)
- 39conditional probability of A given BP(A|B) = P(AB)/P(B)
- 40Then A and B are independent events if and only if either of the following statements is trueP (A|B) = P (A) OR P (B|A) = P (B)
- 41Product rules==
- 42Law of Total Probability==
- 43Bayes Theorem==
- 44Random variables=
- 45Probability functions==
Informationen
- Beschreibung
- Karteikarten am Probability, erstellt von Neja Cesnik am 28/09/2018.
- Erstellt von
- Neja Cesnik
- Aufrufe
- 1
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