4-3 (15) A random variable X has a density given by fX (x) = (1 x2)[u(x) u(x 1)]+ a6(x 2) where u(x) is the unit step function and 5(x) is a delta function. a). Find the value of a, E(X) and a}? b). Find and make a labeled sketch of FX (x) . b). W = the event {X 2 0.5}. Find fX (x | W) and E (X | W) , carefully indicating the domain of all functions where needed