Likelihood function. Comparing estimator MSE.

Consider a sample of size n=8 from the Uniform(θ,θ+4) distribution where θ>0.
Consider two estimators of θ:

T1=X¯ T2=5X¯

(where X¯ denotes the sample mean). By comparing the corresponding MSEs, establish whether T1 is better than T2 to estimate θ.

I wanted to ask you an opinion about this exercise. I cannot understand .

Ok, I know that for compute MSE for T1 for example,


Hence it suffices to compute Var(T1) and E(T1−θ)
To compute Var(T1):


To evaluate the term above, assume Xi
are i.i.d from Uniform(θ,θ+4).


After you compute the two MSE value, I choice the one with smaller mean square error.
I don't undetstand how evaluate and what values ​​can assume the term Xi from Uniform(θ,θ+4) for compute my MSE. Can you help me?
Ok, I know:
If Xi∼Uniform(a,b), then Var(Xi)=(b−a)^2/12 and E(Xi)=(a+b)/2.

So with U(θ,θ+4)



Var(T1)= (4/3)/8=1/6


For E(x)=(θ+θ+4)/2=θ+2

= 1/6 + ((θ+2)-θ)^2
= 25/6

So I think is this MSE of T1 And The same for The second estimator.
Anyway T1 is better than t2 because the T2 mean is 5X right?
Well this is how I compute It...