Prove that for fixed t the counting process N(t) has Poisson distribution with parameter at, i.e. N(t) Poisson(at) (Prove that the sum of two exponentially distributed rv-s has gamma distribution, i.e. X,Y Exp(a) X+Y~ Gamma(2, a); prove that 2 (at)ne-at P(N(t) = n) = Poisson(at)) n! T thus N(i)