Probability Flashcards
number tween 0 and 1 that indicates how likely an event is to happen
probability
all possible outcomes of an experiment
sample space
outcome of an experiment
event
repetition of an experiment
repetition of the experiement
process that produces results of a certain random distribution
experiment
of events / total # of outcomes (part/whole)
probability
probability of one event occuring
marginal probability
event that cannot be broken down into other events
elementary event
P of one event or the other or both happening
union probability
P of both events happening
joint probability
how is marginal P of A written?
P(A)
how is union P of A and B written?
P(A U B)
how is joint P written?
P (A and B) or P (A udU)
how is conditional probability written?
P (A given B) or P( A | B)
probability of A happening given that B has happened
conditional probability
greek letter for sample space
omega
What each repetition of an experiment called?
trial
if the occurrence of one event precludes another
mutually exclusive events
2 or more events that have no effect on the probability of occurrence of either
independent events
the occurrence of one event does change the other event
dependent events
2 events that encompass one sample space but have no intersection between them
complementary events
general law of addition
P(A U B) = P(A) + P(B) - P(A and B)
read –> P A union B = marginal A + marginal B - P (A intersection or joint or udU B)
general law of multiplication
P (A and B) = P(A) * P (B | A)
read –> joint probability is marginal P of A times P (B given A)
Why is the intersection subtracted from the general law of addition?
so that only one intersection from each sample space is counted
How does the general law of multiplication change if A and B are independent events?
P (A and B) = P(A) * P (B | A) becomes
P (A and B) = P(A) * P (B)
What is probability-weighted average of the possible outcomes of a random variable?
expected value
What is variance in terms of expected value?
expected value of the squared deviations subtracted from the variable’s expected value
what is the measure of joint variability of two random variables?
covariance
what is the scaled variation of joint variability of two random variables?
correlation
what is the difference in covariance and correlation?
both show a relationship but correlation allows the strength of that relationship to be assessed
variable that contains the outcome of a chance experiment
random variable
2 types of random variables
- discrete random variable
- continuous random variable
random variable with only whole numbers as out comes + example
discrete random variable - dice, coins, choosing people
random variable that can have decimals as outcomes + example
continuous random variable - investment returns
math function that provides probabilities of occurrence of different possible outcomes in an experiment
probability distribution
the probability that a random variable takes a specific value
probability function
describe probability function as it concerns discrete vs continuous variables
discrete variable - probability of a variable being a specific number
continuous variable - probability of a variable falling in a specific range
name discrete distributions:
- bernoulli distribution
- binomial distribution
- poisson distribution
- hypergeometric
distribution base on an experiment with only two possible outcomes “win or lose” + example
bernoulli distribution - coin flips
distribution based on repeated experiments described by bernoulli distributions + example
binomial distribution - repeated coin flips
describes distribution regarding probability of having a number of events within a certain space of time or area + example
poisson distribution - number of calls between 9a-5p or number of bacteria per square inch
what is the difference between binomial and hypergeometric distributions?
binomial - sampling with replacement
hypergeometric - sampling without replacement
name continuous distributions
- uniform distribution
- exponential distribution
- normal distribution
- lognormal distribution
distribution where all the events share the same probability
uniform distribution
related to poisson distribution
exponential distribution
What is the difference between poisson and exponential distribution?
poisson has a certain number of occurrences in a time period
exponential answers the probability of how frequent those occurrences are
what question does exponential function help answer and what is the greek letter associated?
what is the rate of failure = mu
bell curve
normal distribution
describe bell curve
symmetric where the mean equals the mode, unimodal
what is the area under a normal curve?
1
distribution that has a long tail and asymmetric bulk and follows a natural logarithm
lognormal distribution
