M_S2013 Problem 1: X is a Poisson r.v. with rate of 3 per sec, following the Poi

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M_S2013

Problem 1: X is a Poisson r.v. with rate of 3 per sec, following the Poisson arrival process. (a) Find the probability of no arrivals during a 10 msec interval (b) Find the mean of the number of arrivals in 10 msec (c) Find the Variance of the number of arrivals in the same interval (d) If A = (more than 10 arrivals in 1 sec} and B = (more than 5 arrivals in 1 sec}, find P(X|A^c intersection B) where X relates to a 1 sec interval. (e) Find E(X|A^c intersection B). (f) Find Var(X|A^c intersection B) (g) Find Var(X|A)

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