Fundamentals of Probability and Statistics for Engineers

3.2.2 PROBABILITY MASS FUNCTION FOR DISCRETE RANDOM

VARIABLES

Let be a discrete random variable that assumes at most a countably infinite
number of values 1 2 ,... with nonzero probabilities. If we denote
1, 2,.. ., then, clearly,

1

8

–2 –1 0 1 2 3

x

1

1

2

FX(x)

Figure 3.1 Probability distribution function of for Example 3.1

0.2

1.0

–1 01

FX(x)

x

Figure 3.2 Probability distribution function of a continuous random variable

Random Variables and Probability D istributions 41

X,FX 9 x),

X,FX 9 x)

X

x,x
P 9 Xˆxi)ˆp 9 xi),iˆ

0 <p…xi† 1 ;for all i;

X

i

p…xi†ˆ 1 :

9

=

;

… 3 : 4 †