Page 214 - Fundamentals of Probability and Statistics for Engineers

Some Important Continuous Distributions 197

Its corresponding PDF is

" 2 #
x
1 Z u m†
F X x†ˆ 1=2 exp 2 du; 1 < x < 1; 7:10†
2 † 1 2
which cannot be expressed in closed form analytically but can be numerically
evaluated for any x.
The pdf and PDF expressed by Equations (7.9) and (7.10), respectively, are
graphed in Figures 7.6(a) and 7.6(b), respectively, for m ˆ 0 and ˆ 1. The

f X (x)

0.399

x
– 4 – 3 – 2 – 1 0 1 2 3 4
(a)
F X (x)

1

x
– 4 – 3 – 2 – 1 0 1 2 3 4
(b)

Figure 7.6 (a) Probability density function, f (x), and (b) probability distribution
X
function, F X (x), of X for m ˆ 0 and ˆ 1

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