Let (Nt)t≥0 be a Poisson process. Explain what is wrong with the following proof that N3 is a constant. E ((N3)2) = E(N3N3) = E(N3(N6-N3))                 = E(N3)E(N6-N3) = E(N3)E(N3)                 = E(N3)2. Thus, Var(N3) = E((N3)2)-E(N3)2=0, which gives that N3, is a constant with probability 1.

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