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,

E((T1−θ)^2)=Var(T1−θ)+E2(T1−θ)

=Var(T1)+E2(T1−θ)

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

To compute Var(T1):

Var(T1)=Var(∑Xi/8)

To evaluate the term above, assume Xi

are i.i.d from Uniform(θ,θ+4).

Similarly,

E(T1−θ)=E(∑Xi/8)−θ

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?