Page 365 - Fundamentals of Probability and Statistics for Engineers

348 Fundamentals of Probability and Statistics for Engineers

140

120
y = + x β ^
α
^
(g/cm 2 ) 100

Young's modulus, y 80 ^ ^ σ ^ σ

60

40

20

0
10 20
2
Stress, x (g/cm )
Figure 11.3 Estimated regression line and observed data, for Example 11.3
. Result i: let 2 be the unbiased estimator for 2 as defined by Equation
c
(11.33), and let

n 2†
c 2
D ˆ : 11:34†
2
It follows from the results given in Section 9.3.2.3 that D is a 2 -distributed
random variable with (n 2) degrees of freedom.

. Result ii: consider random variables
1=2
8 9
" #" # 1
n n
< X X 2 =
^
A † c 2 x 2 n x i x† ; 11:35†

i
iˆ1 iˆ1
: ;

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