A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 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.
anonymous
 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.

This Question is Closed

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

anonymous
 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\[P(X1+X2=k)=\sum_{m}^{?}P(X1=m)P(X2=km)\]=\[\sum_{m=0}^{k}\lambda^m1*e^(\lambda1)/(m!) *\lambda^m2*e^(\lambda2)/((km)!) \] =\[e^(\lambda1+\lambda2)/k!\sum_{m=0}^{k}k!/(m!(km)!*\lambda^m1\lambda^(km)2\]=\[e^(\lambda1+\lambda2) /k! *(\lambda1+\lambda2)^k\]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.