Suppose that, over a given period of time, Y denotes the simple returns of a stock and X the returns of the market index in which the stock is listed. The coefficient of the stock is defined as

B$=\frac{\text{C}\text{o}\text{v}[X,Y]}{V[X]}$

and measures the volatility or systematic risk of that stock compared to the market in which it is listed. In other words, it indicates how the stock's return is expected to vary relative to the average market return. If p$($X$,$ Y$)=0\mathrm{.}8,$ SD$[$X$]=0\mathrm{.}1,$ and V$[$Y$]=0\mathrm{.}0225,$

a$)$ What is the value of the coefficient B$?$

b$)$ What are the maximum and minimum values that can reach B$?$