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# Consider a Poisson process with rate . Let N be the number of arrivals in time interval (0,t]andM...

- Consider a Poisson process with rate λ. Let N be the number of arrivals in time interval (0,t]andM bethenumberofarrivalsintimeinterval(0,t+s],wheret>0,s≥0.

(a) Find the conditional PMF pM |N (m | n) of M given N .

(b) Find the joint PMF pN,M(n,m) of N and M.

(c) Find the conditional PMF pN|M(n|m) of N given M.

(d) Find E[NM].