Statistics Homework Solutions 43

Statistics Homework Solutions 43 - 43 SUPPLEMENTARY...

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Unformatted text preview: 43 SUPPLEMENTARY EXERCISES FOR CHAPTER 2 0 98 0 985 0 985. ¡¥ ¨ ¤ ¦¥ ¨ ¤ ¡ 0 985 0 95 0 7 0 9997. ¨ ¢ ¨ ¢ ¨ ¡¥ 0 98 07 ¨ ¨ ¤ ¡¥ ¥ ¤ ¥ ¡ ¤ ¢¥ PA BPC D 0 95 ¤ ¥ ¤ ¡ ¤ ¡¥ ¥ ¤ ¤ ¡ ¢¥ ¥ ¡ ¤ ¤ ¢¥ ¡ £¥ ¡ ¤ ¡¥ ¤ ¥ ¤ ¤ Let A denote the event that the resistance is above specification, and let B denote the event that the resistance is below specification. Then A and B are mutually exclusive. ¨ ¡¥ ¤ 0 15 0 6667 ¨ ¡ ¢¥ ¤ 0 10 0 15 0 10 ¢ ¨ ¨ ¡ ¡¥ ¥ ¥ ¤ PB PA B 0 05 ¨ ¤ ¤ ¡ ¡ ¢¥ PB A B PA B PB ¡ ¤ ¥ ¤ ¡ ¡ ¢¥ ¡ ¤ (b) P B A B PA ¨ (a) P(doesn’t meet specification) = P A B ¤ Let R be the event that the shipment is returned. Let D1 be the event that the first fuse chosen is defective, let D2 be the event that the second fuse chosen is defective, and let D 3 be the event that the third fuse chosen is defective. Since the sample size of 3 is a small proportion of the population size of 10,000, it is reasonable to treat these events as independent, each with probability 0.1. ¡¥ P D c Dc Dc 1 2 3 1 ¡ ¡ ¤ ¡ ¡ 1 ¤ ¡¥ P Rc 09 ¥¨ ¤ ¡ 1 3 ¡ ¡¥ PR 0 271. ¨ 5. PCPD ¡ PC D PD ¤ PA B PC ¨ CD PC D ¤¥ PD ¡¥ ¨ PA B 3. PC ¨ PC D ¤ (If dependence is taken into account, the answer to six significant digits is 0.271024.) 7. Let A be the event that the bit is reversed at the first relay, and let B be the event that the bit is reversed at the second relay. Then P bit received is the same as the bit sent P A c Bc PA B P A c P Bc 2 0 12 PAPB 09 0 82. 9. Let A be the event that two different numbers come up, and let B be the event that one of the dice comes up 6. Then A contains 30 equally likely outcomes (6 ways to choose the number for the first die times 5 ways to choose the number for the second die). Of these 30 outcomes, 10 belong to B, specifically (1,6), (2,6), (3,6), (4,6), (5,6), (6,1), (6,2), (6,3), (6,4), and (6,5). Therefore P B A 10 30 1 3. ¢¥ ¤ ¥ ¤ ¡¥ ¡ ¤ ¢¥ ¤ ¡ ¡¥ ¤ ¨ £ ¡ £ ¡¥ ¤ ¡ ¨ ¢ ¨ ¡¥ ¤ ¥ ¤ ...
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