ap stat unit 5-6 formula test

σ^2= Var(X)= Σ (X-μ)^2 ⋅ P(X)

variance for a random var, X

Z= (X-μ)/ σ

z-score

P(A∪B) = P(A) + P(B)

addition for disjoint/mutually exclusive events

P(X=k)= nCk ⋅ p^k (1-p)^n-k

binomial model

μ = E(x) = np

binomial μ

σ = SD(X) = √np(1-p)

binomial σ

P(A^c) = 1 - P(A)

complement rule

P(A|B)= P(A∩B) / P(B)

conditional probability

μ = E (X) = ΣX ⋅ P(X)

expected value for a random var, X

P(A∪B) = P(A) + P(B) - P(A∩B)

general addition rule

P(X=n) = (1-p)^n-1 ⋅ p

geometric model

μ= E(X) =1/P

geometric μ

σ = SD(X) = √(1-p) / p

geometric σ

P(A∩B)= P(A|B) ⋅ P(B)

intersection of conditional events (aka- general multiplication rule)

P(A∩B)=P(A) ⋅ P(B)

intersection of independent events

P(A∩B)= 0

mutually exclusive/disjoint- NO OUTCOMES in common

SD (X+/- Y)= √SD^2(X) + SD^2(X)

pythagorean theoream of statistics

σ= SD (X)= √var(X)

standard deviation for a random var, X

(P(x) ≤ 0.05)

statistically significant

P(A|B)= P(A)

test for independence