$**$ Please answer the question accurately showing step$-$by$-$step solution by hand.

NO EXCEL allowed.

P$.$S$.$: Use the appropriate Statistical tables if needed. $**$

You believe that the daily variance of returns of the S&P $500$ Index follows a GARCH$(1,1)$ process and run the following

model:

${}_t^2=$hat$({)}_1+$hat$({)}_2(x_{t-1}-(\stackrel{}{x}){)}^2+$hat$({)}_3{}_{t-1}^2+e_t$

And get the following Regression Results:

a$)$ What is the model's mean reverting level?

b$)$ What is the annualized standard deviation assuming $250$ trading days in the year?