3) (7+3=10) This question has two independent sub-parts (i) and (ii). (i) Let U be a Uniform random variable on the interval [-1,1] a) Compute E(U), Var(U), E(U+). b) Find the CDF and PDF of U2. Is the distribution of UZ Uniform on (0,1)? (ii) Let X be a r.v. with E (X) = /, and a CDF F which is continuous and strictly increasing. Consider the inverse function F-1 . (F-1 is called a quantile function, with lots of applications in statistics). Find the area under the curve of the quantile function between 0 to 1 (in terms of At)