By Fearn T., Brown P.J., Besbeas P.

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14, 702, 688. If the first and the second job are assigned to production line II, the number of assignments is 18! ×6! = 14, 702, 688. If the first and the second job are assigned to production line III, the number of assignments is 18! ×4! = 10, 501, 920. Therefore, the answer is 14, 702, 688 + 14, 702, 688 + 10, 501, 920 = 39, 907, 296. (c) The answer is 133, 024, 320 − 39, 907, 296 = 93, 117, 024. 256 44 CHAPTER 1. 25 Let W be the event that ‘the team wins the game’ and let S be the event that ‘the team has a player sent off ’.

25. 43. 42. 99. 6 (a) E(X 2 ) = 4 2 0 x Then E(X) = x 8 8 3 Var(X) = 8 − 8 9 (b) σ = dx = 8 so that 8 3 2 = 98 . 25 gives x = 2. 46. 46. 0115. 217. 401. 184. 63 64 CHAPTER 2. 985. 288. 385. 097. 8. 50. 93. 43.

3 (a) Since 0 −2 15 64 + x 64 dx = 7 16 9 8 + and 3 0 3 8 + cx dx = 9c 2 it follows that 7 16 + 9 8 + 9c 2 =1 which gives c = − 81 . 2. 5 (a) Since F (∞) = 1 it follows that A = 1. Then F (0) = 0 gives 1 + B = 0 so that B = −1 and F (x) = 1 − e−x . 5054. 06315 55 56 CHAPTER 2. 361. 54 × 10−5 . 09. 2. 11 (a) Since 11 10 Ax(130 − x2 ) dx = 1 it follows that A= 4 819 . 283 57 58 CHAPTER 2. 77 If $9 is paid to play the game, the expected loss would be 23 cents. 3. 31. If you can play the game a large number of times then you should play the game as often as you can.

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