Let X1,X2,X3,Y1,Y2,Y3 be random variables.

If X1 and Y1 have the same distribution,

X2 and Y2 have the same distribution,

X3 and Y3 have the same distribution,

then is it true that X1+X2+X3 and Y1+Y2+Y3 will have the same distribution? Why or why not?

Any help is appreciated!