Question

Consider four random variables (SEE PIC FOR EASY TO READ)
x1,x2,x3,x4
where
X1+X2,X3,X4
are independent.
It holds that
∑i=14Xi
~Possion (10) and
X3
~Possion (3) and
X4
~Possion (3)

Prove or disprove:
The distribution of
X1+X2
can be detremined