Fundamentals of Probability and Statistics for Engineers

resulting in

The desired answer is, using Equation (7.50) and Table A.3,

where

H ence,

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

where ( ) is the well-known gamma function:

212 Fundamentals of Probability and Statistics for Engineers

Yexp

^2 lnY

2



ˆ 300 ;

exp…^2 lnY†ˆ

4  104

9  104

‡ 1 ;

Yˆ 250 ;

lnYˆ 0 : 61 :

)

… 7 : 51 †

P…Y> 400 †ˆ 1 P…Y 400 †ˆ 1 FY… 400 †

FY… 400 †ˆFU

1

0 : 61

ln

400

250



ˆFU… 0 : 77 †ˆ 0 : 7794 :

P…Y> 400 †ˆ 1  0 : 7794 ˆ 0 : 2206 :

… 7 : 52 †

fX…x†ˆ



…†

x^1 ex; forx 0 ;

0 ; elsewhere;

8

><

>:

… 7 : 52 †



…†ˆ

Z 1

0

u^1 eudu; … 7 : 53 †