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we known that for independent Poisson distributed random variables that X 1 Poisson( 1 ) X 2 Poisson( 2 ) and it holds that X

we known that for independent Poisson distributed random variables that

X1 Poisson(1)

X2 Poisson(2)

and it holds that X1 + X2 Poisson(1 + 2)

Show that if Xi P oisson(i), i = 1, 2, . . . , k are independent then the conditional distribution of X1 given X1 + X2 + . . . Xk is Binomial and determine the parameters of this Binomial distribution

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