Studied by 19 people
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)
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
Note 
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