III. CDFS AND EXPECTATIONS Let X be a random variable defined by the pdf fx(x) = x][u(x) - u(x - 1)] + ad(x -2), where u(x) is the unit step function which is equal to 1 when a 2 0 and 0 otherwise, and 6(x) is the impulse function (Dirac delta function) which is the (generalized) derivative of u(I). a) Find a, E[X ] and Var[X] b) Define the event W = {X > 0.5}. Find P[X IR that satisfies f(t)at = Fxw(I) VIER We can call this a conditional PDF given W. Find the set of all r e R over which your function f satisfies f(x) > 0. This is often called the "support" of the function