Unit 1 & 2

Question 1

If every element of a set A is also an element of set B, then A is a ______ of B.

Answer 1

subset

Question 1

A _____ is a collection of objects; the objects are called _____.

Answer 1

set; elements

Question 2

If A is a subset of B and B is a subset of A, the two sets are _____.

Answer 2

equal

Question 3

The ________ is a set with no elements.

Answer 3

null set

Question 4

A ________ contains all objects conceivably of interest in a particular context.

Answer 4

universal set

Question 5

If a set contains a finite number of elements, we call the set _______.

Answer 5

finite

Question 6

If a set contains infinitely many elements that we can list distinctly, we call the set ________.

Answer 6

countably infinite

Question 7

If the elements of a set take a continuous range of values and cannot be written as a list, we call the set ________.

Answer 7

Uncountable

Question 8

The ______ of a set A, with respect to universe omega, is the set of all elements of omega that do not belong to A.

Answer 8

complement

Question 9

The ______ of sets A and B is the set of all elements that belong to A or B (or both).

Answer 9

union

Question 10

The ______ of sets A and B is the set of all elements that belong to both A and B.

Answer 10

intersection

Question 11

Two sets C and D are called ______, or mutually exclusive, if their intersection is empty.

Answer 11

disjoint

Question 12

A collection of sets is a ______ of a set S if the sets in the collection are disjoint and their union is S.

Answer 12

partition

Question 13

The underlying process is called an ________, and it will produce exactly one of the possible _______.

Answer 13

experiment; outcome

Question 14

The set of all possible outcomes is called the __________, and a subset is called an ________.

Answer 14

sample space; event

Question 15

What is this probability axiom?

P(A) >= 0 for every event A.

Answer 15

non-negativity

Question 16

What is this probability axiom?

If A and B are disjoint events, P(A U B) = P(A) + P(B).

Answer 16

additivity

Question 17

What is this probability axiom?

For sample space S, P(S) = 1.

Answer 17

normalization

Question 18

What does it mean for two events to be independent?

Answer 18

the occurrence of one event doesn’t affect the probability of the other’s occurrence

Question 19

What is a permutation?

Answer 19

a selection of k objects from n objects when order of the selection matters

Question 20

What is a combination?

Answer 20

a selection of k objects from n objects when order of the selection doesn’t matter

Question 21

What is a random variable?

Answer 21

a real-valued function of the experimental outcome

Question 22

What is a discrete random variable?

Answer 22

a random variable that can take a finite or countably infinite number of values

Question 23

What does the probability mass function describe?

Answer 23

the distribution of a discrete random variable

Question 24

When do you use the Bernoulli Distribution?

Answer 24

when there is only one “trial” and the outcome of the trial is a success of failure

Question 25

When do you use the Binomial Distribution?

Answer 25

when there are n independent Bernoulli trials and each has a probability of success

Question 26

When do you use the Geometric Distribution?

Answer 26

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.

Question 27

When do you use the Poisson Distribution?

Answer 27

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.

Question 28

What is an expected value?

Answer 28

the mean of a random variable that describes the center of the its distribution

Question 29

What is a variance of a random variable?

Answer 29

describes the spread, or the dispersion, of the distribution