ISyE 2027 EXAM 1 Questions And Answers With Latest Updates

ISyE 2027 EXAM 1
mutually exclusive - ✔️✔️two or more events are said to be mutually exclusive when at
most one of the events can be true
EiEj = ∅ whenever
i =/ j which means that the events are disjoint sets

partition - ✔️✔️collection of subsets. If A is an event, then A and A^c form a partition of
Ω

De Morgan's Law - ✔️✔️the complement of the union of two sets is the intersection of
the complements ((A ∪ B)^c = A^cB^c) and VICE VERSA: the complement of the
intersection is the union of the complements ((AB)^c = A^c ∪ B^c)


∪ - ✔️✔️OR - UNION

B^c - ✔️✔️COMPLEMENT OF B


probability space - ✔️✔️(Ω, F, P)
Each ω of Ω - outcome
P - probability measure on F

event axioms - ✔️✔️the set of events F is required to satisfy the event axioms

probability axioms - ✔️✔️the probability measure P is required to satisfy the axioms

sample space - ✔️✔️Ω - set of possible outcomes

event - ✔️✔️F - subset of Ω. An event is said to occur or be true when the experiment
is performed if the outcome is in the event

∩ - ✔️✔️AND - INTERSECTION
(this can also be written as A∩B = AB)