02_01 - Sample Space and Events p 2-1 Sample Space the set...

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p. 2-1 Sample Space and Events Sample Space : the set of all possible outcomes in a random phenomenon. Examples: 1.Sex of a newborn child: = {girl, boy} 2.The order of finish in a race among the 7 horses 1, 2, …, 7: = {all 7! Permutations of (1, 2, 3, 4, 5, 6, 7)} 3.Flipping two coins: = {(H, H), (H, T), (T, H), (T, T)} 4.Lifetime of a transistor: = [0, ) Event : Any (measurable) subset of is an event. Examples: 1. A ={girl}: the event - child is a girl. 2. A ={all outcomes in starting with a 3}: the event - horse 3 wins the race. 3. A ={(H, H), (H, T)}: the event - head appears on the 1st coin. 4. A =[0, 5]: the event - transistor does not last longer than 5 hours. an event occurs: outcome the event Q : How many different events if # = n < ? p. 2-2 • Set Operations of Events Union. C : either A or B occurs Intersection. C : both A and B occur Complement. C : A does not occur Mutually Exclusive. A and B have no outcomes in common. Definitions of union and intersection for more than two events can be defined in a similar manner • Some Simple Rules of Set Operations Commutative Laws. Associative Laws. Distributive Laws. DeMorgan’s Laws. A B = B A and A B = B A ( n i =1 A i ) c = n i =1 A c i and ( n i =1 A i ) c = n i =1 A c i . A B = ∅⇒ C = A c C = A B C = A B ( A B ) C =( A C ) ( B C ) ( A B ) C = A ( B C ) .

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02_01 - Sample Space and Events p 2-1 Sample Space the set...

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