Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
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
|
|
Zα
|
means that the Φ(z) = α
|
|
Φ(Zα) =
|
1 - α
|