Karteikarten
BTRY Prelim 1
Karten in diesem Stapel (12)
- 1probability (event)how "likely" the event is to occur?
- 2experimentany process, real or hypothetical, in which the possible outcomes can be identified ahead of time
eg. toss a coin ten times; observe the lifetime of a tv - 3eventa well defined set of possible outcomes of the experiment; a subset of the sample space (think of an event as a set)
eg. I see at least 4 heads; TV doesn't last longer than 5 years; sum of dice equals 3: E={(1,2),(2,1)} c("subset of") S - 4sample spacethe collection of all possible outcomes of an experiment (a set)
eg. sample space associated with tossing two dice: S={(i,j); i,j in {1,2,3,4,5,6}} - 5basic set theory- A c B if forall x in A => x is in B (B "contains" A, A "included in" B)
- A = B iff AcB and BcA
- A set that contains no elements is called the empty set 0 with slash - 6finite setset that has finitely many elements
- 7countable infinite setif there is a one-to-one correspondence between the set's elements and the set of real numbers {1,2,3,...,n,...}
- 8complement (A^c) of set AAcS; the set that contains all elements of S that are not in A
- 9union of sets A and Bthe set that contains the elements of A alone, of B alone, and those that belong to both A and B; AuB
- 10intersection of sets A and BAnB, the set that contains elements common to both A and B
- 11disjoint/mutually exclusive setsif they have no elements in common; AnB=empty set (0 slash)
- 12properties of sets and of operations with sets1.) A c B and B c C, then A c C, for any A,B,C
2.) empty set c A, for any A
3.) (A^c)^c = A, for any A c S, for some S
4.) For any sets A and B (included in some generic set S)
(a) A u B = B u A
(b) A u A = A
(c) A u A^c = S
(d) A u empty set = A
(e) A u S = S
(f) if A c B, then A u B = B
4'.) for any A,B,C we have: AuBuC = (AuB)uC = Au(BuC)
5.) for any sets A,B,C (c S) we have:
(a) AnB = BnA
(b) AnA = A
(c) AnA^c = empty set
(d) Anempty set = empty set
(e) AnS = A
(f) if AcB, then AnB = A
(g) AnBnC = (AnB)nC = An(BnC)
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- Computer Science Karteikarten am BTRY Prelim 1, erstellt von Sonia Appasamy am 21/02/2017.
- Erstellt von
- Sonia Appasamy
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