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Each one of particles are randomly placed in 2 cells. Supose that and for we call...

Each one of N particles are randomly placed in 2 cells. Supose that N\sim Poisson(\lambda ) and for k=1,2 we call X_{k} to the number of particles placed in the cell number k .

Prove that the random variables X_{1} and X_{2} are independent and each one have Poisson distribution.

(Note: Please no unreadable handwriting, thumbs up restricted to a good answer. Thankyou.)

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