Exam 2 Flashcards
probability
quantifies long-term randomness
law of large numbers
as n increases, proportion of occurrences of a given outcoe approaches a particular number
relative frequency
large number of trials to find long run proportion of outcomes
probability experiment
chance process leading to well-defined outcomes
outcome
result of a trial of a probability experiment
sample space
set of all possible outcomes
event
subset of a sample space
corresponds to a particular outcome or group of outcomes
3 basic interpretations of probability
classical
empirical (relative frequency)
subjective
complement
set of all outcomes not included in event
intersection of 2 events
outcomes in 2 different events
union of 2 events
outcome in one event or the other
disjoint events
do not have any common outcomes
mutually exclusive
conditional probability
reduction of sample space by imposing a condition
2 ways to check if two events are independent
if either are true, they are independent
fundamental counting rule
in a sequence of n events in whcih the first has k1 possibilities, the second has k2 and so on, the total number of possibilities of the sequence will be
k1k2k3…kn
sensitivity
p(POS|S)
positive test given state present
specificity
p(NEG|S^c)
negative test given state not present
permutation
arrangement of objects in a specific order
combination
grouping of objects where order does not matter
random experiment
function that assigns a numerical value to each simple event in a sample space
the random variable reflects…
the aspect of the experiment that is of interest to us
X refers to…
random variable itself
(ex. number of heads in 3 coin flips)
x refers to…
a possible value of the random variable
probability distribution
specifies a random variable’s possible values and their respective probabilities
standard deviation formula for probability distribution
4 requirements for binomial distribution
- fixed number of trials, n
- each trial has only 2 outcomes, success or failure
- outcomes must be independent
- probability of success must be the same for each trial
poisson used for…
rare events
events occurring over time
lambda
rate
adjust for interval given
for poisson, rate = lambda = ? = ?
rate = lamda = mean = variance
format for hypergeometric distribution
explain hypergeometric distribution
distribution of a variable that has 2 outcomes when sampling is done without replacement
for hypergeometric,
x = 0, 1, 2, 3…min(….)
x = 0,1,2,3…min(a, n)
explain geometric distribution
an experiment with 2 outcomes that is repeated until a success
for geometric,
x =
number of trials until first success
shape parameter for normal distribution
standard deviation
shift/location parameter for normal distribution
mean
empirical rule: 1 standard deviation away
68% of data
16% on either side
empirical rule: 2 standard deviations away from mean
95% of data
2.5% on either side
empirical rule: 3 standard deviations away from mean
99.7% of data
0.15% on either side
unique to standard normal distribution
mean = 0
standard dev = 1
arguments for normalcdf
normalcdf(-10,000, x, 0, 1) = area
arguments for invNorm
invNorm(area, 0, 1) = z
sampling distribution
probability distribution that specifies probabilities for the possible values a statistic can take
sampling distribution helps predict…
how close a statistic falls to the parameter it estimates
mean and standard deviation trend for samples
formula for standard deviation of sample
standard error
standard deviation of sample
as sample size increases…
standard error decreases
central limit theorem
sampling distribution is always normal if n ≥ 30, no matter the shape of the original distribution
(also works sometimes with a smaller n)
