JP CH 4: Probability: An Introduction to Modeling Uncertainty

A probability law used to compute the probability of the union of events

Two events: P(AUB) = P(A) + P(B) - P(A n B)

Two mutually exclusive events: P(A n B) = 0, so P(AUB) = P(A) + P(B)

A method used to compute posterior probabilities

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

Skewed bell curve

something either happens or does not happen (yes/no, sale/no sale)

the event consisting of all outcomes that are not in A

the probability of an event given that another event has already occurred

when the probability of one event is dependent on whether some related event has already occurred

a random variable that may assume any numerical value in an interval or collection of intervals

can include negative & positive infinity

on a continuum

ex. how many secs ppl look @ an ad, time, weight, distance, temperature-→ shaded area on a chart

a probability distribution for a discrete random variable for which each value Xi that the random variable assumes is associated with a defined probability f(Xi)

a random variable that can take on only specified discrete values

ex. flip a coin-→[0,1], if heads,0, if tails, 1

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

rectangle shape

ex. if you roll a die, even chance for every #

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

A collection of outcomes

a measure of the central location, or mean, of a random variable

the average

ex. expected values helps banks determine their cash flow & seeing if they get at least a payment a month from mortgages they have

A continuous probability distribution that is useful in computing probabilities for the time it takes to complete a task or the time btwn arrivals

mean & STD are equal to each other

Two events A & B are independent when the events do not influence each other

the event containing the outcomes belonging to both A & B

A n B

the probability of two events both occurring; the probability of the intersection of two events

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

events that have no outcomes in common

A n B is empty & P(A n B) = 0

no overlap

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

z-score

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

has to do w approaching a stopping point

expected value = avg. (mean) & the one below it

not a normal distribution bc not symmetrical & slightly skewed

revised probabilities of events based on additional information

initial estimate of the probabilities of events

a numerical measure of the likelihood that an event will occur

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

equal to the sum of the probabilities of outcomes for the event

a process that generates well-defined experimental outcomes

on any single repetition or trial, the outcome that occurs is determined by chance

a numerical description of the outcome of an experiment

the set of all outcomes

positive square root of the variance

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

rectangle shaped

continuous

the event containing the outcomes belonging to A or B or both

A U B

a measure of the variability, or dispersion, of a random variable

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