Question $3$

Consider the Density function of Gaussian $($Normal$)$ Density.

$f(x_i|)=\frac{1}{\sqrt[\phantom{2}]{2{}_1}}*e^{-\frac{(x_1-{}_0{)}^2}{2{}_1}}$

where ${}_0$ represents $()$ and ${}_1$ represent ${}^2({}^2).$ Below is the Likelihood function

$L()=pro{d}_i=1^{n}f(x_i|)$

Consider the given density and likelihood function, and answer the following question

Derive the equation for maximum likelihood estimates $($MLE$)$ of $({}_0)$ and ${}^2({}_1)$ by

maximizing the likelihood function.

Taking into consideration the equations you derive just above for $({}_0)$ and ${}^2({}_1),$ calcu$-$

late the values for $$ and ${}^2$ when the data is $x=[-5,7,9,12,-17,1,4,24,0,3]$