Page 229 - Fundamentals of Probability and Statistics for Engineers

212 Fundamentals of Probability and Statistics for Engineers

2
ln Y
Y exp ˆ 300;
2
4 10 4
exp 2 †ˆ ‡ 1;
ln Y 9 10 4
resulting in

)
Y ˆ 250;
7:51†
ln Y ˆ 0:61:
The desired answer is, using Equation (7.50) and Table A.3,

P Y > 400†ˆ 1 P Y 400†ˆ 1 F Y 400†

where

1 400
F Y 400†ˆ F U ln
0:61 250
ˆ F U 0:77†ˆ 0:7794:

Hence,

P Y > 400†ˆ 1 0:7794 ˆ 0:2206:

7.4 GAMMA AND RELATED DISTRIBUTIONS

The gamma distribution describes another class of useful one-sided distribu-
tions. The pdf associated with the gamma distribution is

8
> 1 x ; for x 0;
< x e
f x†ˆ † 7:52†
X
>
0; elsewhere;
:

where ( ) is the well-known gamma function:
Z 1
e du;
†ˆ u 1 u 7:53†
0
7:52†

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