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Math
Probability
Probability Theory
AP Statistics CB Unit 4+5: Probability, Random Variables, Probability Distributions, Sampling Distributions
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Terms in this set (37)
probability
measure of the likelihood of an event
sample space
set of all possible outcomes of an experiment
tree diagram
representation useful for determining the sample space for an experiment when there are relatively few possible outcomes
event
outcome or set of outcomes or a random phenomenon; subset of the sample space
impossible event
if an event can never occur
p=0
sure event
if an event must occur every time
p=1
odds in favor of an event
ration of the probability of occurrence of an event to the probability of nonoccurrence
complement
set of all possible outcomes in a set that do not lead to the event
disjoint/mutually exclusive events
have no outcome in common/cannot occur together
THEY ARE DEPENDENT
union
set of all possible outcomes that lead to at least one of the 2 events
intersection
set of values that lead to both events A and B
conditional event
set of outcomes for event A if event B has occurred
independent
when the occurrence of one event doesn't depend on the occurrence of the other
dependent
if the probability of an event changes if the other event occurs
union/addition rule
if disjoint, you don't have to subtract the overlap
intersection/multiplication rule
probability of A times the probability of B given A
conditional probability/bayes theorem
intersection with independence
variable
quantity whose value varies from subject to subject
probability experiment
experiment whose possible outcomes may be known but whose exact outcome is a random event and cannot be predicted with certainty in advance
random variable
a numerical description of the outcome of an experiment
discrete random variable
quantitative variable that takes a countable number of values (no decimals)
continuous random variable
quantitative variable that can take all the possible values in a given range (decimals)
probability distribution of a discrete random variable/discrete probability distribution
table, list, graph, or formula giving all possible values taken by a random variable and their corresponding probabilities
expected value
mean of a discrete random variable x
multiply each value of the random variable by its probability and add together
combination
number of ways r items can be selected out of n items if order of selection is not important
binomial distribution
distribution of a discrete random variable
binomial distribution conditions
- n repeated trials of a number fixed in advance
- 2 possible outcomes (success or failure)
- all trials are identical and independent
geometric distribution features
- n repeated trials
- each trial has 2 possible outcomes (success or failure)
- trials are repeated until a predetermined number of successes is reached
- all trials are identical and independent
probability distribution of a continuous random variable
graph or formula giving all the possible values taken by a random variable and corresponding probabilities
bell curve/Gaussian distribution
names for the normal distribution
standard normal
normal distribution with mean 0 and SD of 1
z score
transformation of any variable to standard normal
parameter
numerical measure of a population
statistic
numerical measure of a sample
sample distribution
probability distribution of all possible values of a statistic
standard error
standard deviation of the distribution of a statistic
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