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Inter event times Q 4.1

N

Nimisha

Member
Hi
Please explain that in Q 4.1 ii) how will we denote the required probability in terms of T and N.
Is it P(Nt=1)?
Not too clear with this concept.
Thank you.
 
Hello

\( P(N_t = 1) = P(N_t - N_0 = 1) \) is a special case of the probability. More generally, the question is asking you to work out:

\( P(N_{s + t} - N_s = 1) \) for any s >= 0, t > 0

ie for any interval of length t (so from some time s to time s + t) the probably of seeing one arrival in that interval. Due to the nature of a Poisson process, this probability is the same for any s>=0 for some fixed t >0.

For a Poisson process, the distribution of \( N_{s + t} - N_s \) is \( Poi(\lambda t) \) for any s >= 0, t > 0.

Hope this helps

Andy
 
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