Let Nitt 0 be a Poisson Process with rate lambda Can Zt alp

Let {Ni(t),t 0} be a Poisson Process with rate lambda. Can Z(t) = alphaN1(t) + betaV2(i) ever be a Poisson Process, where alpha and beta are some non-zero constants. In other words, are there any values of alpha, beta, and N2(t) such that {Z(t)t 0} is a Poisson Process. Please note that {N2{t),t 0} is not allowed to be either a Poisson Process, and is also not allowed to be a trivial random process (e.g., it is not a constant over all time). Carefully prove or disprove.

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