<Tr> <Th> PGF </Th> <Td> exp ⁡ (λ (z − 1)) (\ displaystyle \ exp (\ lambda (z - 1))) </Td> </Tr> <Tr> <Th> Fisher information </Th> <Td> 1 λ (\ displaystyle (\ frac (1) (\ lambda))) </Td> </Tr> <P> In probability theory and statistics, the Poisson distribution (French pronunciation (pwaˈsɔ̃); in English often rendered / ˈpwɑːsɒn /), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event . The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume . </P> <P> For instance, an individual keeping track of the amount of mail they receive each day may notice that they receive an average number of 4 letters per day . If receiving any particular piece of mail does not affect the arrival times of future pieces of mail, i.e., if pieces of mail from a wide range of sources arrive independently of one another, then a reasonable assumption is that the number of pieces of mail received in a day obeys a Poisson distribution . Other examples that may follow a Poisson include the number of phone calls received by a call center per hour and the number of decay events per second from a radioactive source . </P>

What is the parameter of the poisson distribution
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