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LetX1,X2,...be the inter-arrival times of a Poisson process of rate. LetTn=X1++Xnbe the time of thenth arrival and denote byNtthe number of arrivals by timet(withN0= 0).

  1. LetX1,X2,...be the inter-arrival times of a Poisson process of rate. LetTn=X1++Xnbe the time of thenth arrival and denote byNtthe number of arrivals by timet(withN0= 0). Find, in terms of,

find:

  1. E[N5|N2=4]
  2. P(N2<3|N4=5)
  3. P(T2>3|N1<4)

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