Page 158 - Fundamentals of Probability and Statistics for Engineers

Functions of Random Variables 141

f (y)
Y

2

1

y
0 1 2

Figure 5.17 Probability density function, f (y), in Example 5.11

Y
x
2

R 2
x 1
— = y
x 2

x 1

2

Figure 5.18 Region R in Example 5.12
2
The region R for positive values of x 1 and x 2 is shown as the shaded area in
Figure 5.18. Hence,
Z 1 Z x 2 y
8
f x 1 ; x 2 †dx 1 dx 2 ; for y > 0;
<
F Y y†ˆ 0 0 X 1 X 2
:
0; elsewhere:

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