JP CH 4: Probability: An Introduction to Modeling Uncertainty

ch 4 on business analytics probability & distributions

Addition Law

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)

Bayes’ Theorem

A method used to compute posterior probabilities

Binomial probability distribution

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)

Complement of A

the event consisting of all outcomes that are not in A

Conditional Probability

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

Continuous Random Variable

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

Custom Discrete Probability Distribution

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)

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Discrete Random Variable

a random variable that can take on only specified discrete values

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

Discrete Uniform Probability Distribution

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 #

Empirical Probability 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 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

Exponential Probability Distribution

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

Independent Events

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

Intersection of A & B

the event containing the outcomes belonging to both A & B

A n B

Joint Probabilities

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

Marginal Probabilities

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

Mutually exclusive events

events that have no outcomes in common

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

no overlap

Normal Probability Distribution

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

z-score

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

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

Posterior Probabilities

revised probabilities of events based on additional information

Prior Probability

initial estimate of the probabilities of events

Probability

a numerical measure of the likelihood that an event will occur

probability distribution

a description of how probabilities are distributed over the values of a 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 variables

a numerical description of the outcome of an experiment

sample space

the set of all outcomes

standard deviation

positive square root of the variance

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

rectangle shaped

continuous

Union of A & B

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

A U B

Variance

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

Venn Diagram

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