$$ Question 2. Interarrival times to a coffee shop is random with unknown distribution. A shop owner wants to approximate daily interarrival times using the first 10 arrivals of the day, denoted as $X_{1}, "X_{2}, X_{3}, \ldots, X_{10}$, with one of the following estimators: \begin{array}{c} That{\mu}_{1}=\frac{10 X_{1}+20 X_{3}}{40} \ \hat{\mu}_{2}=0.3 X_{1}+0.5 X_{5}+0.2 X_{10} \ \hat{\mu}_{3}=\frac{4 X_{2}+5 X_{9}}{9} \ What{\mu}_{4}=0.1 X_{4}+0.9 X_{7} \ What{\mu}_{5}=a X_{1}+(1-a) X_{10} \quad \text { where } o\leq a \leq 1 \end{array} $$ a) Determine the bias and precision for each estimator. Write down the MSE expressions. b) Which estimator is better $\hat{\mu}_{1}$ or $\hat{\mu}_{5}$. (Use MSE) SP.JG. 149