Lecture_09_21

Lecture_09_21 - Lecture of September 21 From Last Class...

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1 Lecture of September 21 Lecture of September 21 •F r o m L a s t C l a s s - Normal distribution - Standardized normal variable and Φ ( ) - Two important results • HW#3 due in class on 09/26.

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2 Three shafts are made and assembled in a linkage. The length of each shaft, in centimeters, is distributed as follows: Shaft 1: x 1 ~ N (75, 0.09) Shaft 2: x 2 ~ N (60, 0.16) Shaft 3: x 3 ~ N (25, 0.25) (a) What is the distribution of the linkage length L ? Example 2.7 Example 2.7 1 2 3 x 1 x 2 x 3 L variance σ 2
3 (b) What is the probability that the linkage will be longer than 160.5 cm? Example 2.7 (continued) Example 2.7 (continued) 1 2 3 x 1 x 2 x 3 L

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4 • If (1) (2) x 1 , x 2 , …, x n are normally and independently distributed, (3) x i ~ N (0, 1), i.e., all x i 's are standard normal Then, y follows a (chi-square) distribution Chi Chi Square Distribution Square Distribution (with degrees of freedom (with degrees of freedom n n ) ) 2 2 2 2 1 n x x x y + + + = L 2 n χ • The subscript "
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Lecture_09_21 - Lecture of September 21 From Last Class...

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