Chapter 4

Question 1

Probability

Answer 1

Mathematics describing random behaviors, measuring chances, and quantifying uncertainties

Question 2

Random Phenomenon

Answer 2

Situation in which we know what possible outcomes could happen but we don’t know which ones will happen until they occur

Question 3

Trial

Answer 3

An attempt or random experiment that generates an outcome (flipping a coin once)

Question 4

Probability as a long-term frequency

Answer 4

The probability of any outcome of a random phenomenon is the proportion of times the outcome would occur in a long series of repeated trials

Question 5

Long-term frequency example with a fair coin toss

Answer 5

If you were to toss a fair coin, say, a million times, you would tend toward getting heads 1/2 the time and tails 1/2 the time. Thus the probability of getting either can be said to be 1/2.

Question 6

Sample Space

Answer 6

Set of all possible outcomes

Question 7

Dice Sample Space

Answer 7

{1,2,3,4,5,6}

Question 8

Pop quiz example with three questions (C, I) _ _ _

Answer 8

2^3 possibilities since there are 2 choices (Correct, Incorrect) for each of the 3 slots. So there are 8 possibilities in all

Question 9

Event

Answer 9

Any outcome or set of outcomes of a random phenomenon; subset of sample space

Question 10

P(A)

Answer 10

Probability of event A

Question 11

Three Axioms of Probability

Answer 11

Question 12

Enumeration Method

Answer 12

Find probability of each individual outcome in sample space and add probabilities of each outcomes event A contains

Question 13

Classical Method

Answer 13

If outcomes are equally likely:

Question 14

Complement of A

Answer 14

All outcomes in sample space not in A

Question 15

Complement of A Formula

Answer 15

Question 16

Disjoint Events (Mutually Exclusive)

Answer 16

A and B are disjoint if they share no common outcomes

Question 17

Disjoint Formula

Answer 17

A and B are disjoint if:

Question 18

Independent Events

Answer 18

A and B are independent if event A never affects probability of event B and vice versa

Question 19

Independence Formula

Answer 19

A and B are independent if:

Question 20

Union of Events

Answer 20

The union of A and B are the outcomes that are in A or B

Question 21

Union Formula

Answer 21

The union of A and B is found as:

Question 22

How often are events Independent?

Answer 22

Not often

Question 23

Independence and Mutual Exclusivity (Disjointness)

Answer 23

They are NOT equal; essentially opposite

Question 24

Random Variable

Answer 24

A numerical measurement of the outcome of a random phenomenon

Question 25

Probability Distribution

Answer 25

Specifies random variables values and corresponding likelihoods

Question 26

Discrete Random Variable

Answer 26

Takes on discrete values

Question 27

For each value in the discrete distribution

Answer 27

Each probability between 0 and 1 and sum up to 1

Question 28

Mean of random variable

Answer 28

The expected value, average value of the random var

Question 29

Mean/E(X) Formula

Answer 29

Question 30

Standard Deviation

Answer 30

Deviation/spread of random variable

Question 31

Standard Deviation Formula

Answer 31

Question 32

Binomial Distribution

Answer 32

Binary (success/failure) trial with n binary trials following number of successes of probability p

Question 33

Binary Trial

Answer 33

One with two possible outcomes

Question 34

Three Binomial Distribution Conditions

Answer 34

1. Each of n trials must have two possible outcomes 2. Each trial has probability p of success and 1 - p of failure 3. The n trials are independent

Question 35

X ~ Binomial( n , p )

Answer 35

X is binomially distributed with n trials each with success probability p

Question 36

Binomial Distribution Formula

Answer 36

Question 37

Binomial Distribution Mean and Variance

Answer 37