probaility & statistics formulas

P(A) ^ P(B)

intersect

A U B

union

A^c = 1-A

complement

A | B = A ^B / B

conditional

n^r

permutation with repetition

n!/(n-r)!

permutation without repetition

n!/r!(n-r)! = n choose r

combinations without repetition

(r + n - 1)/r!(n-1)!

combinations with repetition

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

independence

P(A)P(A|B)

multiplicative law

P(A) + P(B) - P(A ^B)

additive law

(sum from i=1 to k) P(A|B_i)P(B_i)

law of total probability

P(A|Bj)P(B_j) / P(A|B_i)P(B_i)

baye’s rule

(sum of all y) Y * p(y)

expected value of discrete random variable Y

μ

expected value of E(Y) when p(y) is a characterization of the population frequency distribution

(sum of all y) g(y) * p(y)

expected value of real-value function g(Y)

(Y-μ)² /n

variance

E[(Y - μ)²]

variance when expected value = μ

sqrt(V(Y))

standard deviation (σ) when expected value = μ

σ²

population variance

C

expected value of constant C

c * E(g(Y))

expected value of constant C * real-value function