Bayesian Inference Flashcards
“x e A” reads
“x in A”
x is an element of the set A
What is does the symbol of “upside down A” read
For all/ any
What does the “:” semi-colon read?
such that
it is incredibly useful when we want to make statements about a specific group of elements within a set
What is the definition of a subset?
a subset is a set that is fully contained in another set
T or F - If every element of A is also an element of B then A is a subset of B
True
What is this symbol? ⊆
subset symbol
What are the 2 subsets that every set contains?
The set itself
and the null set
Which of the following is true about events?
a) There always exists a set of outcomes that satisfy a given event.
b) The outcomes of an event always have to be numerical.
c) We denote events with lower-case letters of the Latin alphabet like “x” or “y”.
d) We denote individual solutions to these events with upper-case letters from the Latin alphabet like “X” or “Y”.
a) There always exists a set of outcomes that satisfy a given event.
What are the 3 ways events can interact or be represented?
- Never touch
- Intersect
- Completely overlap
What happens when the event circles never touch?
The two events can never happen simultaneously
Event A occurring guarantees that event B is not occurring and vice versa
If two events (circles) intersect, can these events occur at the same time?
Yes
Which of the following does not describe two events with overlapping sets of outcomes?
Being European and being male.
Being white and being French.
Eating meat and being vegan.
Living in Ohio and liking country music.
Eating meat and being vegan.
If two events can occur at the same time, then their respective circles would…
completely overlap.
partially overlap (intersect).
not touch at all.
be tangent to one another.
partially overlap (intersect).
When we want set A and set B to happen at the same time, what are we talking about?
Their intersection
What does the intersection of two events contain?
All the outcomes that are favorable for both event A and event B simultaneously
How is two intersecting sets denoted?
A ∩ B
What is the intersection called of two non overlapping sets?
The empty set
A ∩ B = ∅ or {}
There are no outcomes which satisfy both events simultaneously
When do we use intersections?
only to denote when instances where both events A and B happen simultaneously
Mark the FALSE statement. If we know that “a is in A” and “b is in the intersection of A and B”, then:
A contains a
b is part of the intersection of B and A
B contains b
a is part of B
a is part of B
Mark the pair of sets, whose intersection is NOT the null set.
Odd numbers and even numbers.
Non-positive numbers and non-negative numbers.
Negative and positive numbers.
Numbers divisible by 2 and odd numbers.
Non-positive numbers and non-negative numbers.
Which of the following showcases the two sets, whose intersection is the smaller set.
Black cards and Clubs.
Aces and Jacks.
Queens and Spades.
Diamonds and Hearts.
Black cards and Clubs.
Set A and set B intersect. What happens if we require only one set to occur? What is this called?
A union
What is the union of a set?
a combination of all outcomes preferred for either A or B
Example, if you think of the US as the Union, each state as the Set, then each Element would be what?
The citizens of each state
How is the union of two sets denoted?
A∪B
What is the formula for unions?
The union of A and B = A + B - their intersection
A ∪ B = A + B - A ∩ B
