Can someone explain the condition (ii) of Poisson process? P(N(t + h) = r | N(t) = r ) = 1- lambda h + o(h) P(N(t + h) = r + 1|N(t) = r ) = lambda h + o(h) P(N(t + h) > r + 1|N(t) = r ) = o(h) (Note that a function f (h) is described as o(h) if lim h-->0 [f(h)/h] = 0) How this came? And how to deduce this: "Condition (ii) states that in a very short time interval of length h, the only possible numbers of events are zero or one. Note that condition (ii) also implies that the number of events in a time interval of length h does not depend on when that time interval starts."
As \(\lamda \) is a mean for a time..... Therefore for small time interval h mean is \(\lamdah \) Now for first part Probability of occurring zero is \(e^{-\lamdah}=1- \lamdah + o(h) \) And for second Probability of occurring one is \(\lamdah*e^{-\lamdah}= \lamdah + o(h) \)
