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57 Cards in this Set

  • Front
  • Back
descriptive statistics
summarizes info, data, etc.
inferential statistics
infers characteristics of a population by studying sample characteristics
population
set of experimental units you want to learn about
parameter
descriptive measure of a population, found with a census usually
census
a query of every experimental unit, usually not practical, therefore samples are used
sample
a subset of the population
variable
the number of properties associated with the experimental units
simple random sampling
where every subset of the population is equally likely to be drawn as part of the sample
mode
value occurring most often
median
half the data is less than and half is greater than this piece of data, also known as the second quartile
first quartile
one quarter of the data is less than and three quarters of the data is greater than this piece of data
third quartile
three quarters of the data is less than and one quarter of the data is greater than this piece of data
Box and whisker plot
shows minimum, Q1, Q2, Q3, and maximum, has box around the quartiles and whiskers extending to the min/max
measures of centrality
mode, median, quartiles, mean
measures of variability
range, inter-quartile rage, lower limit, upper limit
mean
average, sum of total parts divided by number of parts
range
maximum - minimum
inter-quartile range
Q3-Q1
lower limit
Q1 - 1.5(IQR)
Upper Limit
Q3 + 1.5(IQR)
population variance
σ^2=Σ(x-μ)^2/ N
sample variance
s^2=Σ(x-μ)^2/ (n-1)
sample standard deviation
(s^2)^.5
population standard deviation
(σ^2)^.5
z-score
(data - mean) / (standard deviation)
sample space (omega)
all the possible outcomes of a probabilistic experiment
event
any subset of the sample space, may be a collection of outcomes
frequentist definition of probability
probabilities will converge to a specific ration if the number of trials approaches infinity almost surely (law of large numbers)
Bayesian definition of probability
probability is a subjective measure of the likelihood of an event happening
axiomatic definition of probability
depends of clear cut, mathematical models
complement of A
everything that is not A
union (of A and B for example)
an event consisting of all outcomes in A, B, or both
intersection (of A and B for example)
and event consisting of all the outcomes occurring simultaneously in A and B
General Additive Principle
for events A and B- P(AuB) = P(A) + P(B) - P(AnB)
combinatorial probability principle
P(A)= lAl / lΩl
Permutation (# of k-length permutations of an n-element set)
n! / (n-k)!
Combination (# of k-element subjects of an n-element set)
n! / k!(n-k)!
Probability of A given B
P(AlB) = P(AnB) / P(B)
Probabilistic Independence
P(AnB) = P(A) x P(B)
P(AlB) = P(A)
P(BlA) = P(B)
random variable
the assignment of a number to each outcome of a sample space
probability distribution of a discrete random variable "X"
a list of all the values the random variable can assume and their associated probabilities
discrete random variable
they take on countably many values (ex. Poisson or binomial)
continuous random variables
can take on a continuum of values (ex. height)
expected value - E(X)
Σx[P(X=x)]
VarX
Σ(x-μ)^2 [P(X=x)]
standard deviation of a random variable
(VarX)^.5
Binomial Distribution
X~Bin(n,p)
probability of a binomally distributed event to occur
( n C x ) P^x (1-p)^n-x
random variable shortcuts
E(X) = np
VarX = np(1-p)
std. deviation = [np(1-p)]^.5
Poisson random variables
E(X) = λ
X~Poisson(λ)
probability distribution of a Poisson random distribution
P(X=x) = (e^-λ)(λ^x / x!)
Poisson approximation for a binomial
if n>100 and np<10
then X~~Poison(np)
probability of a continuous random variable
= the area of its probability density function
the probability density function
(1/(2π)^.5)(e^(-t/2))
standardizing a number
take the z-score (x-μ) / σ
means that the Φ(z) = α
Φ(Zα) =
1 - α