- #1
nonequilibrium
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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?
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.)
One disposes of a bacterial solution for which one would like to know the density (i.e. the number of bacteria per unit volume). [...] One takes five Petri dishes and fills each Petri dish with 1 ml of the bacterial solution. After a certain incubation time one starts 'counting' the number of bacteria in each of the Petri dishes. [...] In this example we in fact have the situation of a Poisson distribution for which we have (a realization of) a sample of size 5, [itex]X_1, \cdots, X_5[/itex]. The parameter [itex]\theta[/itex] is here the mean density of bacteria per ml solution.
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?