Fundamentals of Probability and Statistics for Engineers

The region R^2 for positive values of x 1 and x 2 is shown as the shaded area in
F igure 5.18. H ence,

y

fY(y)

01

1

2

2

Figure 5. 17 Probability density function, fY (y), in Example 5.11

x 1

x— 2

=y

R^2

x 2

x 1

Figure 5. 18 Region R^2 in Example 5.12

Functions of Random Variables 141

FY…y†ˆ

Z 1

0

Zx 2 y

0

fX 1 X 2 …x 1 ;x 2 †dx 1 dx 2 ; fory> 0 ;

0 ; elsewhere:

8

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