Probability Test 1
Terms
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- What is the aim of probability/stastics?
- To study the population in terms of a (random) sample and use the sample to make inferences about the population.
- Sample space
- the set of all possible outcomes of an experiment
- Outcome vs event
- An outcome is the result of a single trial of an experiment; an even is one or more outcomes of an experiement
- Probability
- P(A)=f/N
- 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. - Permutation vs combination
- Order matters in permutations, not in combinations
- nPr
- n! / (n-r)!
- nCr =(n r)
- nPr / r! = n! / (n-r)! r!
- 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) - Additive Laws of Probability (union)
-
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 - P(A U B U C) = ...
-
... = P(A) + P(B) + P(C) - P(AB)
- P(AC) - P(BC) + P(ABC) - P(A^C) = ...
- ... = 1 - P(A)
- P(ABC)=...
- ... = P(A)P(B|A)P(C|AB)