Can I have a detailed, step-by-step explanation for part(b) of the following question?

Thank you!

1. (a) Let Y1, Y2....Yn be n independent, continuous and identically distributed random vari- ables with common cumulative distribution function Fy (y) and the common proba- bility density function fy(y). Let Y() = min(Y1, Y2....Yn) be the minimum of the random variables Y1, Y2....Yn . (i) Find the cumulative distribution function of Y(1). (ii) Show that the probability density function of Y() is n[1 - Fy(y) ]-Ify(y) (b) The opening price per share Y1 and Y2 of two similar stocks are independent random variables with a density function given by, (y-4) fy (y)= e ;yz4 ; Otherwise (i) Find the probability density function of the price per share that the investor will pay. (ii) Find the expected cost per share that the investor will pay