Statistics Homework Solutions 21

Statistics Homework Solutions 21 - 21 SECTION 2.3 (b) A...

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Unformatted text preview: 21 SECTION 2.3 (b) A forecast of no rain will be correct on every non-rainy day. Therefore the probability is 0.9. Let E denote the event that a board is rated excellent, let A denote the event that a board is rated acceptable, let U denote the event that a board is rated unacceptable, and let F denote the event that a board fails. Then PE 0 3, P A 0 6, P U 0 1, P F E 0 1, P F A 0 2, and P F U 1. ¤ ¨ ¡¥ ¤ ¨ ¡¥ ¤ 0 03. ¨ ¡¥¨ ¤ ¦¥ ¨ ¨ ¤ ¡¥ ¤ ¨ ¡¥ ¤ ¥ ¤ ¡¥ ¡¥ PFEPE P FA P A P FU PU 01 03 02 06 1 01 ¥ ¤ ¥ ¢¥ ¤ ¤ ¤ ¦¥ ¤ ¥¨ ¥ ¢¥ ¨ ¢¥ ¤ ¤ ¤ ¦¥ ¨ ¤ ¥ ¢¥ ¨ ¤ ¤ ¦¥ ¨ ¥ ¨ FEPE FA P A P FU PU 03 06 1 01 ¥ ¤ ¤ ¦¥ ¤ ¥¨ ¥ ¢¥ ¤ ¤ ¤ ¥ ¥¨ ¤ ¢¥ ¨ ¢¥ ¤¥ ¨ ¤ ¦¥ ¨ ¤ ¤ ¥ ¡ ¤ ¤ ¢¥ ¨ ¤ ¦¥ ¨ ¥ ¤ ¡ 01 03 0 12 P P 01 02 ¥ ¡ PFEPE ¤ ¤ ¡ 0 25 ¥ ¤ ¡ ¡ ¤ ¤ ¤ ¡ ¨ Let F denote the event that an item has a flaw. Let A denote the event that a flaw is detected by the first inspector, and let B denote the event that the flaw is detected by the second inspector. P Ac F P F P FPF P Ac F c P F c 01 01 01 01 1 09 0 011 ¥ ¤ ¥ ¥ ¤ ¤ ¢¥ ¤ ¥¨ ¥¨ ¥ ¤ ¦¥ ¨ ¤¥ ¤ ¤ ¢¥ ¨ ¡ ¤¥ ¨ ¥ ¥ ¥ ¥ ¤ ¥ ¤ ¥ ¤ ¤ ¥ ¤ ¡ ¥ ¤ ¤ ¥ ¢¥ ¤ ¥ ¤ ¤ ¥¨ ¥¨ ¤ ¡ ¢¥ ¤¥ ¤¥ ¤ ¥ ¤¥ ¨ ¢¥ ¨ Bc ¤ ¤ ¤¥ ¨ ¤¥ ¨ ¥ ¡ ¤ ¡ ¡ ¤ ¤¥ ¨ ¡ ¨ ¤ ¡ ¤ ¡ ¥ ¤ ¡ ¤ ¨ P A c Bc F P F P FPF P A c Bc F c P F c P Ac F P B c F P F c F P Bc F P F PA P A c F c P Bc F c P F c 01 03 01 01 03 01 1 1 09 0 0033 Ac ¥ ¥ ¤ (b) P F Ac Bc Ac ¤ (a) P F Ac ¥ ¡ ¤ 25. ¡¥ (c) P E F 03 01 ¨ (b) P F PE PFE ¤ F (a) P E ¡¥ 23. ...
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