Let {N(t), t [0,)} be a Poisson process with rate . Let p : [0,) [0, 1] be a function. Here we divide

Let {N(t), t ∈ [0,∞)} be a Poisson process with rate λ. Let p : [0,∞) ↦ [0, 1] be a function. Here we divide N(t) to two processes N₁(t) and N₂(t) in the following way. For each arrival, a coin with P(H) = p(t) is tossed. If the coin lands heads up, the arrival is sent to the first process (N1(t)), otherwise it is sent to the second process. The coin tosses are independent of each other and are independent of N(t). Show that N₁(t) is a nonhomogeneous Poisson process with rate λ(t) = λp(t).