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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

This note was uploaded on 03/16/2010 for the course GE 331 taught by Professor Negarkayavash during the Spring '09 term at University of Illinois at Urbana–Champaign.

Ask a homework question - tutors are online