Stat 332 Cards exam 1

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

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

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

difference between sample and population

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

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

variation due to performing the experiment

• Outcome (Dependent Variabel)
• example: mpg

• quantity changed (Independent Variable)
• example: driving style

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

Xbar = 1/n { summation (x_{1 ,} x₂ , ..x_n) }

S²= 1/(n-1) { sum 1 to n (x_i - xbar) } ²

s= { sqrt (s²) }

Middle of ORDERED data

• . .
• . . . ... . .. . .
• ________________

the thing with lots of bars and each represents a spread of values like 6-10 or 11-15

learn how to make these.. IQR?

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

Lits of all possible values

A subset of the Sample Space

• A or B or Both
• "A U B"

• A and B
• "A ∏ B"

• Not A
• A^c

Nothing in Common

• 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)

P(A U B) = P(A) + P(B) - P( A ∏ B)

n1, n2, .....nk

• number of ways to choose within group where order matters
• n! / (n-k)!

n! / (k!(n-k)!)

• P(A l B)
• which is P(A "given" B)

P(A l B) = P(A)

P( A ∏ B) = P(B) x P(A l B)

quantity that takes on different values with different possibilities numerical

discrete, countably infinite possible values

P(x) = P(X=x) = P(X= specific thing)

µ_x = { sum all poss (X x p(x)) }

sigma² = {sum. all possible (x-µ)² x p(x)

• sigma = {sqrt (sigma²)}
• standev disc rand var = sqrt variace disc rand var

Takes on different possible values with different possible probabilities (on the interval)

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

µx = integral -infinity to infinity (x f(x)

sigma2 = {integral -inf to +inf [ (x-µ)2 x f(x) dx] }

sigma = {sqrt (sigma2)}

• P(x) = (1-p if x=0)
• ( p if x=1)

p

p(1-p)

x ~ Binomial (n,p)

• P(x) = (ⁿ_x) p^x(1-p)^n-x if x = 0,1,2....n
• 0 otherwise

µx = np

sigma²_x = np(1-p)

• P(x) = e^-lambda (lambda^x/x!) if x = 0,1,2,....
• 0 otherwise

µx = lambda

sigma²_x= lambda

N is normal, µx = µ ..... sigma² = sigma²

• 68% will fall within 1 standev
• 95% will fall within 2 standev
• 99.7% will fall within 3 standev

table A.2

if take log of lognormal you get normal