Fundamentals of Probability and Statistics for Engineers

and

The range 90 110 corresponds to 19 v 21 in the range space RV .Itis
clear that fV(v) is zero outside the interval 19 v 21. In this interval, since
Equation (5.19) represents a strictly monotonic function, we obtain by means
of Equation (5.12),

where

and

We thus have

and

The pdf of V is plotted in Figure 5.9.

fV(v)

1

19 21

v(volts)

Figure 5. 9 Density function fV (v), in Example 5.5

128 Fundamentals of Probability and Statistics for Engineers

fR…r†ˆ

0 : 005 …r 

90 †; for 90r 110 ;

0 ; elsewhere:



… 5 : 20 †

r 



fV…v†ˆfR‰g^1 …v†Š

dg^1 …v†

dv

(^)
(^)
;^19 v^21 ;
g^1 …v†ˆ
100 ‡ 10 v;
dg^1 …v†
dv

ˆ 10 :

fV…v†ˆ 0 : 005 …

 100 ‡ 10 v 

90 †… 10 †

ˆ 0 : 5 …v 

19 †;for 19v 21

fV…v†ˆ 0 ;elsewhere: