Hello, I'm reading a text about statistics, but I don't understand why Poisson applies. (Note, this is not an assignment or anything like that.) Why would X be Poisson distributed with that parameter theta? The only Poisson that I could find reasonable is modelling X as Poisson distributed with parameter [itex]\lambda t[/itex] where [itex]\lambda[/itex] is the rate of multiplication (of the bacteria), and t is the incubation time (which is mentioned in the quote, but strangely enough does not affect the probability distribution in the above case). Can someone give me their take on the matter?