Chapter 6 Discrete Probability Distributions

Question 1

Random variable

Answer 1

a numerical measure of the outcome from a probability experiment, so its value is determined by chance. Denoted using letters such as X.

Question 2

Probability

Answer 2

deals with experiments that yield random short-term results yet reveal long-term predictability.

Question 3

Outcome

Answer 3

The result of a probability experiment.

Question 4

Law of Large Numbers

Answer 4

As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome.

Question 5

Experiment

Answer 5

Any process with uncertain results (or outcomes) that can be repeated.

Question 6

Sample Space

Answer 6

The collection of all possible outcomes of a probability experiment. Often denoted, S.

Question 7

Event

Answer 7

Any collection of outcomes from a probability experiment. Consists of one outcome or more than one outcome. Denoted using capital letters, such as E.

Question 8

Probability Model

Answer 8

A list of the possible outcomes of a probability experiment and each outcome’s probability.

Question 9

Rules of Probability

Answer 9

1) The probability of the event must be greater than or equal to 0 and less than or equal to 1.
2) The sum of the probabilities of all outcomes must
equal 1.

Question 10

Impossible Event

Answer 10

An event whose probability is 0.

Question 11

Certainty

Answer 11

Am event whose probability is 1.

Question 12

Unusual Event

Answer 12

An event that has a low probability of occurring. Typically, an event with a probability less than 0.05.

Question 13

Equally Likely Outcomes

Answer 13

Each outcome in a probability experiment has the same probability of occurring.

Question 14

Tree Diagram

Answer 14

A diagram used to determine the sample space of a probability experiment.

Question 15

Subjective Probability

Answer 15

The probability of an outcome determined by personal judgement.

Question 16

Disjoint Events

Answer 16

Two events that have no outcomes in common.

Question 17

Mutually Exclusive

Answer 17

Another name for disjoint.

Question 18

Venn Diagram

Answer 18

Events are represented as circles enclosed in a rectangle.

Question 19

Contingency Table

Answer 19

A table that relates two categories of data.

Question 20

Two-Way Table

Answer 20

Another name for a contingency table.

Question 21

Row Variable

Answer 21

The variable that describes each row in the contingency table.

Question 22

Column Variable

Answer 22

The variable that describes each column in the contingency table.

Question 23

Cell

Answer 23

The entry in the contingency table where the value of the row variable and column variable intersect.

Question 24

Complement

Answer 24

Let E denote some event. The complement of E, denoted E^c, are all outcomes in the sample space that are not outcomes in event E.

Question 25

Independent

Answer 25

Two events E and F are independent if the occurrence of event E in a probability experiment does not affect the probability of event F.

Question 26

Dependent Events

Answer 26

Two events E and F are dependent if the occurrence of event E in a probability experiment affects the probability of event F.

Question 27

Conditional Probability

Answer 27

The probability that some event F occurs, given that some other event, E, has occurred. Denoted P(F|E).

Question 28

Factorial Symbol

Answer 28

The symbol, denoted n!, where n is greater than or equal to 0 is an integer. The notation is defined as (1) n! = n(n-1) … 321, (2) 0! = 1, and (3) 1! = 1.

Question 29

Permutation

Answer 29

An ordered arrangement in which r objects are chosen from n distinct (different) objects so that r less than or equal to n and repetition is not allowed. The symbol n^Pr represents the number of permutations of r objects selected from n objects.

Question 30

Combination

Answer 30

A collection without regard to order, in which r objects are chosen from n distinct objects with r less than or equal to n and without repetition. The symbol n^Cr represents the number of combinations of n distinct objects taken r at a time.

Question 31

Discrete Random Variable

Answer 31

A variable that has either a finite or countable number of values. The values of a discrete random variable can be plotted on a real number line with space between each point.

Question 32

Continuous Random Variable

Answer 32

A variable that has infinitely many values. The values of a continuous random variable can be plotted on a real number line in an uninterrupted fashion.

Question 33

Probability Distribution

Answer 33

Provides the possible values of the random variable X and their corresponding probabilities. A probability distribution can be in the form of a table, graph, or mathematical formula.

Question 34

Probability Histogram

Answer 34

A histogram in which the horizontal axis corresponds to the value of the random variable and the vertical axis represents the probability of that value of the random variable.

Question 35

Criteria for a Binomial Probability Experiment

Answer 35

An experiment is said to be a binomial experiment if:

1. The experiment is performed a fixed number of times. Each repetition of the experiment is called a trial.
2. The trials are independent. This means the outcome of one trial will not affect the outcome of the other trials.
3. For each trial, there are two mutually exclusive (or disjoint) outcomes, success or failure.
4. The probability of success is fixed for each trial of the experiment.

Question 36

Excel Format for the BINOM.DIST Function

Answer 36

=BINOM.DIST (no. of successes (x), no. of trials (n), probability of success (p), TRUE or FALSE)

Type FALSE when computing EXACTLY a certain number of successes; type TRUE when computing UP TO and INCLUDING (i.e., accumulating) a certain number of successes.