Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

S

Let X1, X2, and X3 be mutually independent random variables with Poisson distributions having means 2, 1, 4, respectively. Find the moment generating function of the sum Y = X1+X2+X3

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. Zarkon
    Best Response
    You've already chosen the best response.
    Medals 1

    where are you stuck?

    • 2 years ago
  2. S
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't know how to start this. I missed class and I can't find much in the textbook. The poisson mgf is M(t) = e^(lambda((e^t)-1)).. lambda is the mean, but i don't get how to put this all together.

    • 2 years ago
  3. Zarkon
    Best Response
    You've already chosen the best response.
    Medals 1

    mgf of a sum of independent rv is the product of the MGF's

    • 2 years ago
  4. S
    Best Response
    You've already chosen the best response.
    Medals 0

    O, so does this mean I should plug in each mean into the formula and multiply them all together?

    • 2 years ago
  5. Zarkon
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

    • 2 years ago
  6. S
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh ok, thank you!

    • 2 years ago
  7. Zarkon
    Best Response
    You've already chosen the best response.
    Medals 1

    yw

    • 2 years ago
  8. Zarkon
    Best Response
    You've already chosen the best response.
    Medals 1

    here is the property I was referring too. http://en.wikipedia.org/wiki/Moment-generating_function#Sum_of_independent_random_variables

    • 2 years ago
  9. S
    Best Response
    You've already chosen the best response.
    Medals 0

    I kinda get it but i get confused with so many letters. X stands for my M(t) and what does a stand for then?

    • 2 years ago
  10. S
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1332814695156:dw| I started with this but I'm not sure if this is the way.. do I also plug in 1 2 and 3 for t? Do I also multiply it by a since it's in the property? =\

    • 2 years ago
  11. Zarkon
    Best Response
    You've already chosen the best response.
    Medals 1

    \[M_{Y}(t)=\mathbb{E}[e^{Yt}]=\mathbb{E}[e^{(X_1+X_2+X_3)t}]\] \[=\mathbb{E}[e^{X_1t+X_2t+X_3t}]=\mathbb{E}[e^{X_1t}e^{X_2t}e^{X_3t}]\] \[=\mathbb{E}[e^{X_1t}]\mathbb{E}[e^{X_2t}]\mathbb{E}[e^{X_3t}]\] \[=M_{X_1}(t)M_{X_2}(t)M_{X_3}(t)\]

    • 2 years ago
  12. Zarkon
    Best Response
    You've already chosen the best response.
    Medals 1

    you have it

    • 2 years ago
  13. Zarkon
    Best Response
    You've already chosen the best response.
    Medals 1

    you can simplify that

    • 2 years ago
  14. S
    Best Response
    You've already chosen the best response.
    Medals 0

    Oooooo ok, that breakdown explains it, ok, i see now, thank you very very much!

    • 2 years ago
  15. S
    Best Response
    You've already chosen the best response.
    Medals 0

    Yea, I'll go on with the simplification, i just wasnt sure if this is where i start.

    • 2 years ago
  16. Zarkon
    Best Response
    You've already chosen the best response.
    Medals 1

    The sum of independent poissons is poisson

    • 2 years ago
  17. S
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks a lot! I wish i could give you another medal =D

    • 2 years ago
  18. Zarkon
    Best Response
    You've already chosen the best response.
    Medals 1

    ;)...yw

    • 2 years ago
    • Attachments:

See more questions >>>

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.