EXAMPLE 4.1b Suppose that an individual purchases two electronic components each of which may be either defective or acceptable. In addition, suppose that the four possible results —

(d, d ),

(d, a),

(a, d ),

(a,

a) — have respective probabilities .09, .21, .21, .49

[where

(d, d ) means that both components are defective,

(d,

a) that the first component is defective and the second acceptable, and so on]. If we let X denote the number of acceptable components obtained in the purchase, then X is a random variable taking on one of the values 0, 1, 2 with respective probabilities

If we were mainly concerned with whether there was at least one acceptable component, we could define the random variable I by

If A denotes the event that at least one acceptable component is obtained, then the random variable I is called the indicator random variable for the event A, since I will equal 1 or 0 depending upon whether A occurs. The probabilities attached to the possible values of I are

P{X = 0} = .09 P{X = 1}= .42 P{X=2} = .49