Page 145 - Fundamentals of Probability and Statistics for Engineers

128 Fundamentals of Probability and Statistics for Engineers

and
0:005 r
90†; for 90 r 110;

f r†ˆ 5:20†
R
0; elsewhere:
The range 90 r 110 corresponds to 19
v 21 in the range space R V . It is
v
clear that f (v) is zero outside the interval 19 21. In this interval, since
V
Equation (5.19) represents a strictly monotonic function, we obtain by means
of Equation (5.12),

1

1

f v†ˆ f ‰g v†Š dg v† ; 19 v 21;
R
V
dv

where

1
g v†ˆ
100 ‡ 10v;
and

1
dg v†
ˆ 10:
dv
We thus have
f v†ˆ 0:005
100 ‡ 10v
90† 10†
V
ˆ 0:5 v
19†; for 19 v 21

and
f v†ˆ 0; elsewhere:
V
The pdf of V is plotted in Figure 5.9.

f (v)
V

1

v(volts)
19 21

Figure 5.9 Density function f (v), in Example 5.5
V

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