Prove that for fixed t the counting process N(t) has Poisson distribution with parameter at, i.e....

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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) 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)

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To prove that the counting process Nt has a Poisson distribution with parameter at we need to show that PNt n ateat n The counting process Nt represen... View the full answer