Modeling Uncertainty Flashcards
Addition law
P(A Union B) = P(A) + P(B) - P(A Intersection B)
Bayes’ Theorem
P(A|B) = P(B|A)P(A)/P(B); posterior equals prior times likelihood over marginal
Binomial probability distribution
A probability distribution for a discrete random variable showing the probability of x successes in n trials
complement of an event
The event consisting of all outcomes that are not in a given event
Conditional probability
The probability of an event given that another event already occurred
Continuous random variable
A random variable that may assume any numerical value in an interval or collection of intervals. An interval can include negative and positive infinity.
Custom discrete probability distribution
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
Discrete random variable
A random variable that can take on only specified values.
discrete uniform probability distribution
A probability distribution in which each possible value of the discrete random variable has the same probability.
Empirical probably distribution
A probability distribution for which the relative frequency method is used to assign probabilities.
Event
A collection of outcomes
Expected value
A measure of the central tendency of a random variable.
Exponential probably distribution
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.
Independent events
Two events that do not influence each other; their probabilities do not change given the other happened
Intersection of events
The event containing outcomes that occur in two given events
Joint probability
The probability of two events both occurring; in other words, the probability of the intersection of two events.
Marginal probability
The values in the margins of a joint probability table that provide the probabilities of each event separately.
Multiplication law
P(A Intersection B) = P(B)P(A|B) = P(B|A)P(A)
Mutually exclusive events
Events with no outcomes in common, produces an empty intersection
Normal probability distribution
A continuous probability distribution in which the probability density function is bell-shaped and determined by its mean mu and standard deviation sigma
Poisson Probability Distribution
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.
posterior probability
Revised probability of an event based on additional information
prior probability
Initial estimate of the probability of an event
Probability
A numerical measure of the likelihood that an event will occur.
Probability Density Function (PDF)
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.
Probability distribution
A description of how probabilities are distributed over the values of a random variable
Probability Mass Function (PMF)
A function, denoted by f_x, that provides the probability that x assumes a particular value for a discrete random variable.
Probability of an event
Equal to the sum of the probabilities of outcomes for the event.
Random experiment
A process that generates well-defined experimental outcomes. On any single repetition or trial, the outcome that occurs is determined by chance
Random variable
A numerical description of the outcome of an experiment.
Sample space
The set of all outcomes
Standard deviation
The positive square root of the variance
Triangular probability distribution
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.
Uniform probability distribution
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.
Union of events
The event containing the outcomes belonging to each of two given events individually or together
Variance
A measure of the variability, or dispersion, of a random variable, equal to the sum of the squared differences from the mean
Venn Diagram
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.
