Statistics Homework Solutions 70

# Statistics Homework Solutions 70 - 70 CHAPTER 3 Â 0 1 Q...

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Unformatted text preview: 70 CHAPTER 3 Â¡ 0 1. Q Ï€r2 v 100 5. Â¡ Â¨ 2 0 Ïƒv Â¨ Â¡ Â¨ Â¡ (b) r 4 00 Ïƒr 0 04, v âˆ‚Q 2Ï€rv 50 2655 âˆ‚r âˆ‚Q Ï€r2 50 2655 âˆ‚v Â¨ Â¡  Â¨ Â¨ Â¡ Â¡ Â¡ Â¡ Â¨ âˆ‚Q âˆ‚r 2 Â¡ Ïƒ2 v 54 Â¡ Â¢ Â¡ 5 4 m3 /s Â¨ Ïƒv v Â¡ 0 01, Ïƒln v âˆ‚ ln Q âˆ‚r 0 05, Â¨ Â¡ Â¨ Ïƒr r 2 r Â¡ Â¡ Â¡ ln v, Ïƒln r âˆ‚ ln Q âˆ‚v  Â¨ 2 ln r Â¡ Â¡ Â¢ Â¢ ln Ï€ Ïƒln Q . 1 v Â¡ ÏƒQ Q Â¡ (c) The relative uncertainty is ln Q 2 Â¡ 100 5 Ïƒ2 r Â¨ Q âˆ‚Q âˆ‚v ÏƒQ Â¡ Ïƒv v 2 2 22 0 012 Â£Â¢ Â¡ Â£Â¢ Â¢ 22 Â¤ Â¡ Ïƒ2 v Â¨ Ïƒr r 2 0 052 Â¢Â¥ Â¡ Â¢ Ïƒ2 r Â¨ âˆ‚ ln Q âˆ‚v 2 0 054 Â¡ Â¡ âˆ‚ ln Q âˆ‚r Â¨ Â¡ Ïƒln Q Yes, the relative uncertainty in Q can be determined from the relative uncertainties in r and v, and it is equal to 5.4%. Â¡Â¥ Â£ Â£ Â¦Â¥ Â£ Â¤ Â¤ Â¡ Â¡ Â¨ Â¡  Â¨ Â¡ Â§Â¥ Â¨ Â¤ Â¨ Â¨ Â¡ Â¡ Â¥ Â£ Â¦Â¥ Â¤ Â£Â¤ Â¡Â¥ Â£ Â£ Â¦Â¥ Â£ Â¤ Â¤ Â¡ Â¡ Â¨ Â¡  12 Â¨ Â¡ Â§Â¥ Â¨ Â¤ Â¨ Â¡ Â¨ Â¡ Â¡ Â¡ Â¡ Â¡ Â¡ Â¨ Â¡ Â¡ Â¡ Â¨ Â¢ Â¡ Â¡ Â¨ Â¡ Â¡ Â¢ Â¨ Â¡ Â¨ Â¢ Â¨ Â¡ Â£ Â¥ Â¢ Â¡ 1 2345682 0 9451802 1 2345682 0 63. Â¨ Â¨ Â¨ Â¨ Â¢ Â¨ Â¤ Â¨ Â¡ Â¡ Â¢ Â¨ Â¢ Â¢ Â¨ Â¡ Â¢ Â¡ Â¢ k2 Â¢Â¥ Ïƒ2 Â¨ Â¢ Â¢ k1 Â¤ Ïƒ2 k2 Â¨ Â¤ Â¢ Â¡ (d) The value of c is cbest Â¡Â¥ Â¢ Ïƒ2 0 52 1 2345682 0 78 Â¨ 0 52 0 9451802 Â¡ Â¡ Â¨ Â¡ Â¨ 0 2 5 2 Ïƒ2 k2 1 234568. We are using Â¨ Â¨ Â¡ Â¡ Â¡ 1 1 2s 1 0 23 Â¡ 1 50 1 C Â£ Â¨ Â¡ Â¨ Â¡ 1 C0 Â¨ Â¡ 0 0018 ÏƒC 0 0002. k 1t 1C dk 6172 84, Ïƒk ÏƒC 6172 84 0 0002 dC (c) Let k k1 k2 2 0 5k1 0 5k2. From parts (a) and (b), Ïƒk 0 945180 and Ïƒk 1 2 extra precision in Ïƒk and Ïƒk in order to get good precision in Ïƒk . Ïƒk 10 4 0 95 1 50, C 5 2 Ïƒ2 k1 10 04 Â¡ Â£Â¤ 10 4 Â£ Â¦Â¥ Â¤ k Â¥ (b) C0 0 03, t dk 1 dC 50C2 56 Â¡ 0 95 s 1 40 1 C Â£ 10 04 k 1 C0 Â¡ 0 0023 ÏƒC 0 0002. k 1t 1C dk 4725 90, Ïƒk ÏƒC 4725 90 0 0002 dC 40, C Â¨ 19. (a) C0 0 03, t dk 1 dC 40C2 ...
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## This note was uploaded on 12/20/2011 for the course STA 3163 taught by Professor Mattgilg during the Fall '11 term at UNF.

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