Unit 1 & 2 Flashcards
If every element of a set A is also an element of set B, then A is a ______ of B.
subset
A _____ is a collection of objects; the objects are called _____.
set; elements
If A is a subset of B and B is a subset of A, the two sets are _____.
equal
The ________ is a set with no elements.
null set
A ________ contains all objects conceivably of interest in a particular context.
universal set
If a set contains a finite number of elements, we call the set _______.
finite
If a set contains infinitely many elements that we can list distinctly, we call the set ________.
countably infinite
If the elements of a set take a continuous range of values and cannot be written as a list, we call the set ________.
Uncountable
The ______ of a set A, with respect to universe omega, is the set of all elements of omega that do not belong to A.
complement
The ______ of sets A and B is the set of all elements that belong to A or B (or both).
union
The ______ of sets A and B is the set of all elements that belong to both A and B.
intersection
Two sets C and D are called ______, or mutually exclusive, if their intersection is empty.
disjoint
A collection of sets is a ______ of a set S if the sets in the collection are disjoint and their union is S.
partition
The underlying process is called an ________, and it will produce exactly one of the possible _______.
experiment; outcome
The set of all possible outcomes is called the __________, and a subset is called an ________.
sample space; event
What is this probability axiom?
P(A) >= 0 for every event A.
non-negativity
What is this probability axiom?
If A and B are disjoint events, P(A U B) = P(A) + P(B).
additivity
What is this probability axiom?
For sample space S, P(S) = 1.
normalization
What does it mean for two events to be independent?
the occurrence of one event doesn’t affect the probability of the other’s occurrence
What is a permutation?
a selection of k objects from n objects when order of the selection matters
What is a combination?
a selection of k objects from n objects when order of the selection doesn’t matter
What is a random variable?
a real-valued function of the experimental outcome
What is a discrete random variable?
a random variable that can take a finite or countably infinite number of values
What does the probability mass function describe?
the distribution of a discrete random variable
When do you use the Bernoulli Distribution?
when there is only one “trial” and the outcome of the trial is a success of failure
When do you use the Binomial Distribution?
when there are n independent Bernoulli trials and each has a probability of success
When do you use the Geometric Distribution?
when we have a sequence of independent Bernoulli trials each with a probability of success between 0 and 1. This is when the trial is performed until a success is occurred.
When do you use the Poisson Distribution?
when it is used to model counts of occurrences in an interval of time or space. it approximates the binomial PMF when n is large and p is small.
What is an expected value?
the mean of a random variable that describes the center of the its distribution
What is a variance of a random variable?
describes the spread, or the dispersion, of the distribution
