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# CFA: Probability

Addition rule for prob of A or B occurring P(A or B) = P(A) + P(B) – P(AB)
Use multiplication rule for joint probability Prob(AB) = Prob(A|B) × Prob(B)
Multiplication rule for independent probabilities Prob(AB) = Prob (A) × Prob(B)
Probability That at Least One of Two Events Will Occur P(A or B) = P(A) + P(B) – P(AB)
Corr(Ri,Rj) Cov(Ri,Rj) / std(Ri) * std(Rj)
Expected Value E(X) = SUM[P(xi)xi]
Variance SUM[P(xi)[xi – E(X)]^2]
Standard deviation Square root of variance
Portfolio Variance Var(Rp) std^2.a * w^2.a + std^2.b * w^2.b + 2w.a * w.b * Cov.ab --> where Cov.ab = rho.ab * std.a * std.b
Joint Probability Function find out more...
Bayes’ Formula find out more...
Choosing r Objects from n Objects (when order doesn't matter and only 2 possible labels) nCr = n! / [ (n-r)! r!]
Choosing r Objects From n Objects (when order does matter) nPr = n! / (n-r)!
Binomial Random Variable p(x) = [ n!/ (n-x)! x! ] p^x (1-p)^ n-x
probability function p(x) = x / 15 for X = {1,2,3,4,5}  p(3) = 20%
Created by: thongkk