Possion Distribution
Prove or disprove

Question

Possion Distribution
Prove or disprove

anonymous · Answer

Consider four random variables$$x _{1}, x _{2}, x _{3}, x _{4}   $$ where $$ X_{1} + X_{2}, X_{3}, X_{4}$$ are independent. 
It holds that$$\sum_{i=1}^{4} X_{i}$$ ~Possion (10) and $$X_{3}$$ ~Possion (3) and  $$X_{4}$$ ~Possion (3)

Prove or disprove:
The distribution of$$X_{1} + X_{2}$$ can be detremined

anonymous · Answer

@mahmit2012 please help

anonymous · Answer

@Zarkon please help!!!

zarkon · Answer

I would look at the MGF

anonymous · Answer

can you show it

zarkon · Answer

why don't you try first.

anonymous · Answer

I am actually trying to get help for a friend and I am not too familiar with subject but I can try so I am to get the MGF of what part?

zarkon · Answer

what is the MGF of $X_1+X_2+X_3+X_4$


and the MGF of $X_3+X_4$

anonymous · Answer

$$((X2 (-z)+X2-X3 z+X3-X4 z+X4+z))  /  ((z-1)^2)$$

anonymous · Answer

is this the first one?

zarkon · Answer

???

No

anonymous · Answer

ok I have no idea can you help

zarkon · Answer

http://en.wikipedia.org/wiki/Moment-generating_function#Examples

anonymous · Answer

$$e ^{\lambda e^t -1}$$ where t is X1 X2 X3 and X4

zarkon · Answer

$\lambda$ should have a specific value..also t is not X1 X2 X3 and X4

anonymous · Answer

I am really lost with this problem if you could walk the steps out that would be great

anonymous · Answer

Ok I have been fighting with this problem for and hour... will you please show me how to do it I am trying to learn and am getting no where @Zarkon