solve this question

Problem 1 6pts (i) Suppose that Z ~ N(0, 1). Find E[IZ. E[Z-'] and E[Z-1/3], if they exist. 3 pts (ii) Suppose that K is a random variable that only takes values in {0, 1, 2, 3, ...). Show that E[K] = P(K > k). k=0 3 pts (iii) If X ~ Gamma(a, B), find E[Xsex ], specifying the real values of s and t for which it exists. 3 pts (iv) Suppose that a random variable X has the property that, for any a > 1, the conditional dis- tribution of a X given that X > a is the same as the distribution of X. Specify all possible distributions of X (by giving formulas for their c.d.f. or p.d.f.), as well as their expected value