Fundamentals of Probability and Statistics for Engineers

function can be interpreted as the mass density (mass per unit length).
There are no masses attached to discrete points as in the discrete random
variable case. The use of the term is therefore appropriate here
for

Example 3.3.A random variable for which the density function has the
form > 0):

is said to be We can easily check that all the condi-
tions given by Equations (3.11)–(3.13) are satisfied. The pdf is presented
graphically in F igure 3.6(a), and the associated PD F is shown in F igure 3.6(b).
The functional form of the PDF as obtained from Equation (3.12) is

x

ab

fX(x)

Figure 3.5 A probability density function,

fX(x)

x

a

0 1

(a)

FX(x)

0

x

1

(b)

Figure 3.6 (a) Probability density function, and (b) probability distribution

function, for random variable in Example 3.3

Random Variables and Probability D istributions 45

fX 9 x)

fX 9 x)

density function

fX 9 x).

X

9 a

fX…x†ˆ ae

ax; forx 0 ;

0 ; elsewhere;



… 3 : 14 †

exponentially distributed.

fX 9 x),

FX 9 x), X