Poisson distribution - support of the distribution

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"Let N be the number of earthquakes occurring somewhere in the world in a 1-year period"

a) I have decided that this fits a poisson distribution. Is this correct? because they haven't given a mean value?

b) what are the set of values this random variable can take? So the support of the distribution of the random variable. Isn't this just 0 - infinity? how do I write this as an answer?

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See whether the Central Limit Theorem can be used to a good effect. Also, check up the following link: http://www-stat.wharton.upenn.edu/~dsmall/stat510-f05/lectures/notes11.doc