Is a Poisson distribution on ℕ a probability space with the power set as sigma algebra?

[mathisgreat]

probability spaces!

hi!
given poisson distribution in the space 0,1,2,3,... can we check if the distribution is a probability space where sigma algebra is the power set!

 

[mathman]

hi!
given poisson distribution in the space 0,1,2,3,... can we check if the distribution is a probability space where sigma algebra is the power set!

You seem to be confused about definitions of terms: "distribution", "probability space".

For the Poisson distribution, the Pr. space is the set of integers, where the probability of a specific integer is determined by the Poisson. Any collection of integers has a probability defined by adding up the prob. of the integers in the set. Thus the power set is the sigma algebra.

 

[mathisgreat]

thanks..i guess my qn was not at all specific..sorry!