The number of customers Z that arrive at the bank on a certain day is distributed as a Poisson random variable, with (mean) parameter λ > 0. Each custom others, either goes to the teller with probability p, or to the ATM, with probability 1-p (with 0

(a) Find the probability distribution of X. 

(b) Find the probability distribution of Y. 

(c) Are X and Y independent? Explain your reasoning.

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