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

Question

zarkon · Answer

where are you stuck?

s · Answer

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.

zarkon · Answer

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

s · Answer

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

zarkon · Answer

yes

s · Answer

Oh ok, thank you!

zarkon · Answer

yw

zarkon · Answer

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

s · Answer

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?

s · Answer

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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? =\