Ch 1 Flashcards
What is a sample space?
A set whose elements are all possible outcomes to the experiment
What is an event?
A subset A of the sample space
What is the complement of A?
The event that occurs when A does not occur
What is the union of A and B?
The event that occurs when A OR B occurs
What is the intersection of A and B?
The event when both A AND B occur
What is the set difference A\B?
The event that A occurs but B does not
What is a probability measure/function?
A probability measure or probability function P is a map P : A → R that fulfils the properties
1. P (A) ≥ 0 for every event A,
2. P (Ω) = 1 and
3. for countably many disjoint events Ai , i.e. Ai ∩ A j = empty set ; for all i =/j , it holds that P (Ui Ai ) = sigma i P(Ai)
When are events disjoint?
If the intersection is the empty set
What is an alternative to disjoint?
Mutually exclusive. Events that are disjoint can’t both occur
What is P(A^c)? (A complement)
P(A^c)=1-P(A)
If A is a subset of B, express their probabilities as an inequality?
P(A)<=P(B)
What is a discrete uniform distribution?
If for all ω ∈ Ω we have that
P ({ω}) = 1/#Ω ,
then we call this a discrete uniform distribution or uniformly random.
What is P(A) in case of discrete uniform distribution?
P(A)=#A/#omega
How many ways are there to order n objects?
n!
How many combinations are there of selecting k objects out of n with replacement and in order?
n^k
