mean square error comparison

Question

Do you have any idea about how i can solve the question below?

$X_1$ and $X_2$ are random variables that satisfy $E[X_1]=E[X_2]=\mu$ and $Var[X_1]=Var[X_2]=1$. Show that when $|\mu - 10| \leq \frac{\sqrt{6}}{2} $ point estimate $\hat{\mu}_1=\frac{X_1+X_2}{4} + 5$ has a lower mean square error than point estimate $\hat{\mu}_2=\frac{X_1+X_2}{2}$.

Thanks in advance

Answer 1

Hint: Use $$mse(\hat{\theta})=Var(\hat{\theta})+bias^2(\hat{\theta},\theta)$$