Let (Xi)ieN a family of non-negative integer valued random variable with the same probability generating function...

 

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Let (Xi)ieN a family of non-negative integer valued random variable with the same probability generating function G and N another non-negative integer valued random variable independent from the Xi whose probability generating function is H. We define Y=I=1 to N Xi 1. Express the generating function of Y in term of G and H. 2. A flock of birds flies through a field where a bird hunt is taking place. The number of birds in the flock is a Poisson random variable of parameter X > O. Furthermore each bird has a independent probability p > 0 to get shot down. We call Y the (random) number of birds in the flock that survive. Compute P[Y = k] for all integers k 0. Let (Xi)ieN a family of non-negative integer valued random variable with the same probability generating function G and N another non-negative integer valued random variable independent from the Xi whose probability generating function is H. We define Y=I=1 to N Xi 1. Express the generating function of Y in term of G and H. 2. A flock of birds flies through a field where a bird hunt is taking place. The number of birds in the flock is a Poisson random variable of parameter X > O. Furthermore each bird has a independent probability p > 0 to get shot down. We call Y the (random) number of birds in the flock that survive. Compute P[Y = k] for all integers k 0.