Stochastic Processes

The time, • X, between successive arrivals is exponentially distributed, with a cumulative distribution function, F(x), given by

{ }( ) Pr 1 (0 )xF x X x e x−= ≤ = − ≤ < ∞l (6.1) and a probability density function, f(x), given by

( ) ( ) (0 ) xf x F x e x−= = ≤ < ∞′ ll (6.2)

and with a mean, 1

[ ]E X = l

, and a variance, 2 1

[ ]Var X = l

.