MODULUS / REFERENCE
Formulas: Probability theory
Complete Android Modulus reference: formulas for Probability theory.
Combinatorics
• Pn = n!
• Ank = n! / (n − k)!
• Cnk = n! / (k!(n − k)!)
• P = n! / (n1!n2!…nm!) — permutations with repeats
Classical and conditional probability
• P(A) = m / n
• P(A|B) = P(A ∩ B) / P(B)
• P(A ∩ B) = P(B)P(A|B)
Total probability and Bayes
• P(B) = Σ P(Ak)P(B|Ak)
• P(Ai|B) = P(Ai)P(B|Ai) / Σ P(Ak)P(B|Ak)
Random variables and distributions
• E(X) = Σ xipi
• D(X) = E(X²) − (E(X))²
• Pbin(X = k) = Cnk pk(1 − p)n−k
• Ppois(X = k) = e−λ λk / k!
• Pn = n!
• Ank = n! / (n − k)!
• Cnk = n! / (k!(n − k)!)
• P = n! / (n1!n2!…nm!) — permutations with repeats
Classical and conditional probability
• P(A) = m / n
• P(A|B) = P(A ∩ B) / P(B)
• P(A ∩ B) = P(B)P(A|B)
Total probability and Bayes
• P(B) = Σ P(Ak)P(B|Ak)
• P(Ai|B) = P(Ai)P(B|Ai) / Σ P(Ak)P(B|Ak)
Random variables and distributions
• E(X) = Σ xipi
• D(X) = E(X²) − (E(X))²
• Pbin(X = k) = Cnk pk(1 − p)n−k
• Ppois(X = k) = e−λ λk / k!
Values are provided for reference. Check the required unit system and conditions before engineering or laboratory use.