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Population
The entire collection of objects or outcomes about which information is sought

Sample
A subset of a population containing the objects or outcomes that are actually observed.

Simple Random Sample
of size n is a sample chosen by a method in which each collection of n population items is equally likely to comprise the sample, just as in a lottery

Bias
difference between sample and population

Conceptual Population
A population that consists of all values that could possibly be observed, from which a simple random sample comes

Experiment
An experiment is any procedure that can be infinitely repeated and has a well defined set of outcomes

Sampling Variation
variation due to performing the experiment

Response Variable
 Outcome (Dependent Variabel)
 example: mpg

Factor
 quantity changed (Independent Variable)
 example: driving style

Levels
 exact value of the factor
 example: windows up/down

sample mean
Xbar = 1/n { summation (x_{1 , }x_{2 }, ..x_{n}) }

Sampling Variance
S^{2}= 1/(n1) { sum 1 to n (x_{i}  xbar) } ^{2}

Sample Standard Deviation
s= { sqrt (s^{2}) }

Sample Median
Middle of ORDERED data

Dotplot
 . .
 . . . ... . .. . .
 ________________

Histogram
the thing with lots of bars and each represents a spread of values like 610 or 1115

box plot
learn how to make these.. IQR?

Barplot
do instead of piechart each bar is a percent of total observed, so all are < 1

Sample Space
Lits of all possible values

Event
A subset of the Sample Space




Mutually Exclusive
Nothing in Common

Axioms of Probability
 i P(Sample space) = 1
 ii P(A) ≥ 0
 iii if A and B are Mutually Exclusive, P(A U B) = P(A) + P(B)

Additive Rule
P(A U B) = P(A) + P(B)  P( A ∏ B)

Number of ways to perform k tasks
n1, n2, .....nk

Permutation
 number of ways to choose within group where order matters
 n! / (nk)!

Combination
n! / (k!(nk)!)

Conditional Probability
 P(A l B)
 which is P(A "given" B)

Independence
P(A l B) = P(A)

Multiplicative Rule
P( A ∏ B) = P(B) x P(A l B)

Definition of a Random Variable
quantity that takes on different values with different possibilities numerical

Characteristics of a discrete random variable
discrete, countably infinite possible values

Probability Mass FUnction
P(x) = P(X=x) = P(X= specific thing)

Mean of a discrete random variable
µ_{x} = { sum all poss (X x p(x)) }

Variance of a Discrete Random Variable
sigma^{2} = {sum. all possible (xµ)^{2} x p(x)

Standard Deviation of a Discrete Random Variable
 sigma = {sqrt (sigma^{2})}
 standev disc rand var = sqrt variace disc rand var

Characteristics of a Continuous Random Variable
Takes on different possible values with different possible probabilities (on the interval)

Probability Density Function
Probability is Area under P(a < x < b) = {integral a to b ( f(t) dt) }

Mean of a Continuous Random Variable
µx = integral infinity to infinity (x f(x)

Variance of Continuous Random Variable
sigma2 = {integral inf to +inf [ (xµ)2 x f(x) dx] }

Standard dev of a cont random variable
sigma = {sqrt (sigma2)}

Probability Mass Function of Bernoulli (p)
 P(x) = (1p if x=0)
 ( p if x=1)


Variance of Bernoulli
p(1p)

Characteristics of Binomial (n,p)
x ~ Binomial (n,p)

Probability Mass Function of Binomial (n,p)
 P(x) = (^{n}_{x}) p^{x}(1p)^{nx} if x = 0,1,2....n
 0 otherwise

Mean of Binomial (n,p)
µx = np

variance of Binomial(n,p)
sigma^{2}_{x} = np(1p)

Probability mass function of Poisson (lambda)
 P(x) = e^{lambda} (lambda^{x}/x!) if x = 0,1,2,....
 0 otherwise

mean of Poisson (lambda)
µx = lambda

Variance of Poisson (lambda)
sigma^{2}_{x}= lambda

Charactersitics of N (µ,sigma^{2})
N is normal, µx = µ ..... sigma^{2} = sigma^{2}

empirical rule
 68% will fall within 1 standev
 95% will fall within 2 standev
 99.7% will fall within 3 standev


compute probabilities of Lognormal (µ, sigma2)
if take log of lognormal you get normal

