Fundamentals of Probability and Statistics for Engineers

Its corresponding PDF is

which cannot be expressed in closed form analytically but can be numerically
evaluated for any x.
The pdf and PD F expressed by Equations (7.9) and (7.10), respectively, are
graphed in Figures 7.6(a) and 7.6(b), respectively, for m 0 and 1. The

0.399

• 4–3 –2 –1 0 1 2 3 4
  x

fX(x)

FX(x)

1

• 4–3 –2 –1 0 1 2 3 4

x

(a)

(b)

Figure 7. 6 (a) Probability density function, fX (x), and (b) probability distribution

function, FX (x), of X for m 0 and 1

Some Important Continuous Distributions 197

FX…x†ˆ

1

… 2 †^1 =^2 

Zx

1

exp 

…um†^2

2 ^2

"

du; 1<x< 1 ; … 7 : 10 †

ˆ ˆ

ˆ ˆ