Question: If (left(N_{t} ight)) is a Poisson process with rate (lambda), find (a) (Eleft[N_{t+s} mid N_{t} ight]) (b) (Eleft[N_{t} cdot N_{t+s} ight])

If \(\left(N_{t}\right)\) is a Poisson process with rate \(\lambda\), find

(a) \(E\left[N_{t+s} \mid N_{t}\right]\)

(b) \(E\left[N_{t} \cdot N_{t+s}\right]\)

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