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M
 5 years ago
x1 and x2 are indep. random variables with parameter equal to λ1 and λ2. show that sum of x1 and x2 is also a poisson random variable.
M
 5 years ago
x1 and x2 are indep. random variables with parameter equal to λ1 and λ2. show that sum of x1 and x2 is also a poisson random variable.

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mathmagician
 5 years ago
Best ResponseYou've already chosen the best response.0cant remember exactly, but try to use characteristic function

M
 5 years ago
Best ResponseYou've already chosen the best response.0need to use moment generating function approach unfortunatley

mathmagician
 5 years ago
Best ResponseYou've already chosen the best response.0\[P(X1+X2=k)=\sum_{m}^{?}P(X1=m)P(X2=km)\]=\[\sum_{m=0}^{k}\lambda^m1*e^(\lambda1)/(m!) *\lambda^m2*e^(\lambda2)/((km)!) \] =\[e^(\lambda1+\lambda2)/k!\sum_{m=0}^{k}k!/(m!(km)!*\lambda^m1\lambda^(km)2\]=\[e^(\lambda1+\lambda2) /k! *(\lambda1+\lambda2)^k\]
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