Suppose that the number of events occuring in a given time period is a Poisson random variable with parameter ?. If each event is classified as a type i event with probability p_i , i = 1,...,n, ?p_i = 1, independently of other events, show that the numbers of type i events that occur, i = 1,...,n, are independant Poisson random variables with parameters ?, i = 1,...,n.
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