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13 Cards in this Set
- Front
- Back
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What is the aim of probability/stastics?
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To study the population in terms of a (random) sample and use the sample to make inferences about the population.
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Sample space
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the set of all possible outcomes of an experiment
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Outcome vs event
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An outcome is the result of a single trial of an experiment; an even is one or more outcomes of an experiement
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Probability
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P(A)=f/N
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Probability: basic properties
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P(A) is greater than or equal to 0 and less than or equal to one
P(S)=1 p(A1 U A2)=A1 + A2 if A1 and A2 are disjoing, i.e their intersection is the empty set. |
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Permutation vs combination
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Order matters in permutations, not in combinations
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nPr
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n! / (n-r)!
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nCr =(n r)
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nPr / r! = n! / (n-r)! r!
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A and B are independent iff...
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... iff P(AB)=P(A)P(B)
P(A|B)=P(A) P(B|A)=P(B) |
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Additive Laws of Probability (union)
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P(A U B)= P(A)+P(B)-P(AB)
=P(AP+P(B)-P(A)P(B) if A, B independent =P(A)+P(B) if mut exclus |
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P(A U B U C) = ...
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... = P(A) + P(B) + P(C) - P(AB)
- P(AC) - P(BC) + P(ABC) |
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P(A^C) = ...
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... = 1 - P(A)
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P(ABC)=...
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... = P(A)P(B|A)P(C|AB)
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