Sum of two independent poisson random variables


Show that the sum of two independent Poisson random variables has a Poisson distribution. Let X and Y denote two Poisson random variables with parameter Lx and Ly , respectively. Assume that the random variables X and Y are independent. Set Z=X +Y. Prove Z has a Poisson distribution and determine its parameter.

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Basic Statistics: Sum of two independent poisson random variables
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