Exercise 3: Probability: Normal random variables (5 Marks) Let Z be a rv such that Z ~ N(0, 1) (standard normal distribution) and denote and the corre- sponding density and distribution functions respectively. For a set A, define 1A R0,1) as the indicator function of the event, i.e. 0 otherwise Show, and provide justification for your steps/calculations ("no justifications no marks"), that: tip: recall the symmetry properties of the Normal distribution) (b) Show that Ell(Z>-d)-(d), and