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A question on Joint Moment Generating Function Watch

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    The random variables X and Y are defined in terms of the random variable N which is Poisson (lamda): X is Binomial (N, p) and Y = N - X. Show that X and Y are independent, and find their distributions.


    I think we should consider the joint mement generating function in order to prove X and Y are independent, but I get stuck on getting the joint memnt generating funcion.

    Anyone got any clue?
 
 
 
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