Problem 1 Let N(t) be a rate A Poisson process, and let Sn = min{t: N(t) ≥ n} be the time of the nth event. Compute the following: a. E[N(3)] b. Var[N(4)] c. E[S5] d. P(S₂> 4|N(1) = 3)

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Problem 1
Let N(t) be a rate A Poisson process, and let Sn = min{t : N(t) ≥n} be the time of the nth event.
Compute the following:
a. E[N (3)]
b. Var[N(4)]
c. E[S5]
d. P(S₂ > 4|N(1) = 3)
Transcribed Image Text:Problem 1 Let N(t) be a rate A Poisson process, and let Sn = min{t : N(t) ≥n} be the time of the nth event. Compute the following: a. E[N (3)] b. Var[N(4)] c. E[S5] d. P(S₂ > 4|N(1) = 3)
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