Give a proper mathematical explanation, not a statement. Don't give any AI-assisted results.

Problem 2 Let $\overrightarrow{\boldsymbol{X}}=\left\{X_i: i=1, \ldots, n ight\}$ be a random sample from the Normal distribution where $X_i \sim \mathcal{N}(\mu, 1)$ and assume that you estimate parameter $\mu$ using the sample average $\bar{X}$ (which is $\mathcal{N}\left(\mu, \frac{1}{n} ight)$-distributed). From three different samples, you obtain the following estimates $\hat{\mu}_1=1, \hat{\mu}_2=3$, and $\hat{\mu}_3=5$. 1. Calculate the absolute loss for each of the three $\mu$ estimates. 2. Calculate the risk of the estimator given absolute loss. Hint: $\int_{\mathbb{R}} f(x) d x=\int_{-\infty}^c f(x) d x+\int_c^{\infty} f(x) d x$. Hint: The symmetry of the normal distribution as well as substituting $\hat{\mu}-\mu$ during the integration will be helpful.