Probability theory
Poisson distribution
Rare-event probabilities, rates, mean and standard deviation.
Probability theory
Poisson probability of k events
P(X=k)=e⁻λλᵏ/k!→Probability theoryPoisson probability of zero events
P(X=0)=e⁻λ→Probability theoryPoisson: at least one event
P(X≥1)=1−e⁻λ→Probability theoryPoisson: up to k events
P(X≤k)=Σe⁻λλⁱ/i!→Probability theoryPoisson parameter from rate
λ=rt→Probability theoryPoisson mean
μ=λ→Probability theoryPoisson standard deviation
σ=√λ→