Comp 163 final exam formulas

Birthday formula: if N values are chosen from among M, the probability p of no duplicates is (M/M)*(M-1)/M*(M-2)/M*...*(M-N+1)/M. The probability of two values being the same is then 1-p.

Approximate birthday formula: if N values are chosen from among M, the
probability of no duplicates ≃ 1 - N^{2}/2M, for N randomly
distributed choices each in the range 1..M. The approximation is good as
long as N^{2}/2M is small compared to 1. The probability of
duplicates is then N^{2}/2M; again, this is accurate if it is much
less than 1.0.

Bayes formula

Poisson distribution: if the average rate is **
**λ, the probability P of the exact number being k is P(X=k) = **
λ^{k}e^{-λ}/k!**.

Handshaking formula: sum of all vertex degrees is 2*edges

Euler formula: for any planar graph, vertices + faces - edges = 2