Mathematics - Probability and Statistics - Advanced - Probability distributions - Key Distributions

12 steps: (1) DISCRETE DISTRIBUTION: X takes countable values. P(X=x) for each x. ΣP=1. (2) BINOMIAL: X~Bin(n,p). P(X=k)=C(n,k)p^k(1-p)^(n-k). Mean=np, Var=np(1-p). (3) Example: 10 coin flips, P(exactly 7 heads) = C(10,7)(0.5)^10. (4) POISSON: X~Poi(λ). P(X=k)=e^(-λ)λ^k/k!. For rare events. Mean=Var