Modeling Uncertainty

Question 1

Addition law

Answer 1

P(A Union B) = P(A) + P(B) - P(A Intersection B)

Question 2

Bayes’ Theorem

Answer 2

P(A|B) = P(B|A)P(A)/P(B); posterior equals prior times likelihood over marginal

Question 3

Binomial probability distribution

Answer 3

A probability distribution for a discrete random variable showing the probability of x successes in n trials

Question 4

complement of an event

Answer 4

The event consisting of all outcomes that are not in a given event

Question 5

Conditional probability

Answer 5

The probability of an event given that another event already occurred

Question 6

Continuous random variable

Answer 6

A random variable that may assume any numerical value in an interval or collection of intervals. An interval can include negative and positive infinity.

Question 7

Custom discrete probability distribution

Answer 7

A probability distribution for a discrete random variable for which each value x_i that the random variable assumes is associated with a defined probability f_x

Question 8

Discrete random variable

Answer 8

A random variable that can take on only specified values.

Question 9

discrete uniform probability distribution

Answer 9

A probability distribution in which each possible value of the discrete random variable has the same probability.

Question 10

Empirical probably distribution

Answer 10

A probability distribution for which the relative frequency method is used to assign probabilities.

Question 11

Event

Answer 11

A collection of outcomes

Question 12

Expected value

Answer 12

A measure of the central tendency of a random variable.

Question 13

Exponential probably distribution

Answer 13

A continuous probability distribution that is useful in computing probabilities for the time it takes to complete a task or the time between arrivals. The mean and standard deviation for this distribution are equal to each other.

Question 14

Independent events

Answer 14

Two events that do not influence each other; their probabilities do not change given the other happened

Question 15

Intersection of events

Answer 15

The event containing outcomes that occur in two given events

Question 16

Joint probability

Answer 16

The probability of two events both occurring; in other words, the probability of the intersection of two events.

Question 17

Marginal probability

Answer 17

The values in the margins of a joint probability table that provide the probabilities of each event separately.

Question 18

Multiplication law

Answer 18

P(A Intersection B) = P(B)P(A|B) = P(B|A)P(A)

Question 19

Mutually exclusive events

Answer 19

Events with no outcomes in common, produces an empty intersection

Question 20

Normal probability distribution

Answer 20

A continuous probability distribution in which the probability density function is bell-shaped and determined by its mean mu and standard deviation sigma

Question 21

Poisson Probability Distribution

Answer 21

A probability distribution for a discrete random variable showing the probability of x occurrences of an event over a specified interval of time or space.

Question 22

posterior probability

Answer 22

Revised probability of an event based on additional information

Question 23

prior probability

Answer 23

Initial estimate of the probability of an event

Question 24

Probability

Answer 24

A numerical measure of the likelihood that an event will occur.

Question 25

Probability Density Function (PDF)

Answer 25

A function used to compute probabilities for a continuous random variable. The area under the graph of the function over an interval represents frequency of occurrence.

Question 26

Probability distribution

Answer 26

A description of how probabilities are distributed over the values of a random variable

Question 27

Probability Mass Function (PMF)

Answer 27

A function, denoted by f_x, that provides the probability that x assumes a particular value for a discrete random variable.

Question 28

Probability of an event

Answer 28

Equal to the sum of the probabilities of outcomes for the event.

Question 29

Random experiment

Answer 29

A process that generates well-defined experimental outcomes. On any single repetition or trial, the outcome that occurs is determined by chance

Question 30

Random variable

Answer 30

A numerical description of the outcome of an experiment.

Question 31

Sample space

Answer 31

The set of all outcomes

Question 32

Standard deviation

Answer 32

The positive square root of the variance

Question 33

Triangular probability distribution

Answer 33

A continuous probability distribution in which the probability density function is shaped like a triangle defined by the minimum possible value a, the maximum possible value b, and the most likely value m. This distribution is often used when only subjective estimates are available for the minimum, maximum, and most likely values.

Question 34

Uniform probability distribution

Answer 34

A continuous probability distribution for which the probability that the random variable will assume a value in any interval is the same for each interval of equal length.

Question 35

Union of events

Answer 35

The event containing the outcomes belonging to each of two given events individually or together

Question 36

Variance

Answer 36

A measure of the variability, or dispersion, of a random variable, equal to the sum of the squared differences from the mean

Question 37

Venn Diagram

Answer 37

A graphical representation of the sample space and operations involving events, in which the sample space is represented by a rectangle and events are represented as circles within the sample space.