Basic Probability Formulas

 

Probability Range

0 ≤ P(A) ≤ 1

Rule of Complementary Events

P(AC) + P(A) = 1

Rule of Addition

P(A∪B) = P(A) + P(B) - P(A∩B)

Disjoint Events

Events A and B are disjoint iff

P(A∩B) = 0

Conditional Probability

P(A | B) = P(A∩B) / P(B)

Bayes Formula

P(A | B) = P(B | A) ⋅ P(A) / P(B)

Independent Events

Events A and B are independent iff

P(A∩B) = P(A) ⋅ P(B)

Cumulative Distribution Function

FX(x) = P(X ≤ x)

Probability Mass Function

sum(i=1..n, P(X=x(i)) = 1

Probability Density Function

fX(x) = dFX(x)/dx

FX(x) = integral(-inf..x, fX(y)*dy)

FX(x) = sum(k=1..x, P(X=k))

P(a<=X<=b) = integral(a..b, fX(x)*dx)

integral(-inf..inf, fX(x)*dx) = 1

 

Covariance

Cox(X,Y) = E(X-ux)(Y-uy) = E(XY) - ux*uy

Correlation

corr(X,Y) = Cov(X,Y)/(Std(X)*Std(Y))

 

Bernoulli: 0-failure 1-success

Geometric: 0-failure 1-success

Hypergeometric: N objects with K success objects, n objects are taken.

 

 

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