Answers to Exercises Chapter 1 1.2.1 Because B and B c are disjoint events whose union is the whole sample space, the law of total probability (Section 1.2.1) applies to give the desired formula. for x 0; 0 1.2.3 (b) f (x) = 3x 2 for 0 < x < 1; 0 for x 1. 3 (c) E[X] = 4 . 1 4 3 4 26 64 . (d) Pr X = 1.2.4 (b) E[Z] = 9 . 8 (c) Var[Z] = 55 . 64 0 1.2.7 (a) F X (x) = x R 1 for x < 0; for 0 x 1; for 1 < x. (b) E[X] = R/(1 + R). (c) Var[X] = R/ (R + 2)(R + 1) 2 .