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Signals are transmitted according to a Poisson process with rate λ. Each signal is successfully…


Signals are transmitted according to a Poisson process with rate λ. Each signal is successfully transmitted with probability p and lost with probability 1 – p. The fates of different signals are independent. For t ≥ 0 let N1(t) be the number of signals successfully transmitted and let N2(t) be the number that are lost up to time t. (a) Find the distribution of .N1(t),N2(t). (b) What is the distribution of L = the number of signals lost before the first one is successfully transmitted?