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set7solutions - IE 300 GE 331 Discussion Problem Set 7 •...

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Unformatted text preview: IE 300 / GE 331 Discussion Problem Set 7 • 5-40 The graph of the range of , is 1 1 1 2 1 . 2.614 2.649 2 19 8.776 1.852. The correlation coefficient between , and is: 10 2 2 1 1 2/19 Covariance between 2 19 and is 2 19 , 2 19 2 19 2 19 Now, , 8.776 2.614 2.649 9.114. 9.114 8.763 and 8.763 2.649 2.614 2.096 1.930 1.852 0.9206 0 1.930 2.096 • 5-43 1 0 0 1 0, 0 1 1 0 IE 300 / GE 331 Discussion Problem Set 7 1 4 10 0 1 01 1 , 4 2 , 4 1 , 4 10 0 . 1 , 4 2 , 4 1 , 4 . 0 For independence, we need to check whether 0 1 1 , 0 1 1 X and Y are not independent: for example, for 1,0 • C : width of a casing for a door, ~ ~ , 5-60 24, 1/8 1, 1 0. 0 since D: width of a door, ~ Let a) . Then, 23 , 1/16 . . C and D are independent. 24 1 1 0.89 23 b) c) • 5-72 0 0.187 by symmetry and b) . Then, . 0.187 1 8 1 16 5 256 0.1398 a) Let and 1 ∞ . ∞ ∞ Recall Gamma Function: ∞ 1 ! for any integer 3 2! 1, 0. Note that 2 IE 300 / GE 331 Discussion Problem Set 7 , 2/, 1/√2 2 0, , 0. 0. b) for 2 ′ √2 • a) 5-84 : weight of a brick. Let ~ , , 3, 0.25 25 25 3 0.05 denote the mean weight of the 25 bricks in the sample. Then, 25 2.95 3 0.05 25 25 0.0025 , 1 0.159 b) • 5-86 : weight of a candy. . 0.99 ~ , 2.95 . 2.33, 2.8 , 0.1, 0.01. ’s are independent. 16 1.6 a) : Total weight of 16 candies. 16 b) ~ c) If 1.6,0.04 , by symmetry, 17, then 1.7, 1.6 1.6 √0.0017 0.5. 1.7 16 0.01 , 0.04 1.6 √0.0017 2.43 0.0075 ...
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  • Spring '09
  • NegarKayavash
  • Weighted mean, Prime number, Correlation and dependence, Hebrew numerals, Covariance and correlation

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