Poisson point process

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Mean

a 0 , t = ∫ 0 t λ ( α ) d α {\displaystyle a_{0,t}=\int _{0}^{t}\lambda (\alpha )d\alpha }

Variance

a 0 , t + ( a 0 , t ) 2 − ( a 0 , t ) 2 = a 0 , t {\displaystyle a_{0,t}+(a_{0,t})^{2}-(a_{0,t})^{2}=a_{0,t}} since R x ( t 1 , t 2 ) = a 0 , m i n ( t 1 , t 2 ) + a 0 , t 1 a 0…