Statistics I Midterm #2

independent event qualifications

P(A|B) = P(A)
P(B|A) = P(B)

event

collection of sample points

sample space

set of all sample points

event and sample space

event is a subset of sample space

complement features

A U B = S
A ∩ B = { }

mutually exclusive events

cannot occur simultaneously

discrete

finite options

continuous

any number/decimal

discrete uniform distribution function

f(x) = 1/n

binomial distribution

n independent trials with possible success (p) or failure (1-p)

Poisson

estimated number of occurences

normal standard distribution mean

0

normal standard distribution variance

1

binomial E(x)

np

binomial variance

np(1-p)

Poisson E(x)

mu

Poisson variance

mu = mean

continuous uniform distribution function

1/(b-a)

uniform E(x)

(a+b)/2

uniform variance

(b-a)²/12

z-score

Z = (x-mu)/SD

what does z-score do?

changes normal distribution to standard

P(A|B)

P(A∩B)/P(B)

probability distribution features

sigma(f(x)) = 1
1 > f(x) > 0