please solve question 8 on page

Let X be a continuous random variable with the following pidof fox ) = 9 2 70 a ) verify that fox) is the podif of a random variable ie verify pidif properties for for) b ) Find the cidif of *. 8 . Let X be a continuous random variable such that E ( ( x -a ) ? ) for all d. Show that E ( ( x - a ) ? ) is minimized when a = Ecx. Hint : EC (x-a) - E ( ( X - ECX ) ) + ( E ( x ) - a ) ) 2 D Try to minimize this expression