$[5$ points$]$ An asset return $R$ follows the following linear regression model,

$R=+v$

where $vN(0,{}^2)$ and $$ is an unknown constant. A random sample $\{R_1,R_2,$dots,$R_n\}$ is drawn from this model. Answer the following questions.

$(1)$ Write out the OLS estimators of $$ and ${}^2[$No need to derive$].$

$(2)$ Demonstrate that the OLS estimator of $$ is unbiased.

$(3)$ If we test $H_0$:$=10\%$ vs$.H_1$:$10\%,$ write out the test statistic and its distribution under $H_0.$