Sufficient statistic for normal distribution (not iid)

#1
Hello,

I am a bit confused with this exercise, since I never worked with samples of this type. I would appreciate if you can help me. The exercise is as follows:

Let {Xi} ~ N(iθ, 1) for i = 1, .... , n be an independent, but not identically distributed sample. Check that T = ΣiXi it is a sufficient statistic for θ.

Thanks!