Question

A shipment of 6 computers contains three that are slightly defective. A retailer receives three of these computers at random. List the elements of the sample space S using the letter D and N for defective and none defective computers respectively. To each sample point assign a value of X of the random variable X representing which is slightly defective.

Answer 1

As there are three computers of six that are slightly defective, the number of defective computers X among the three purchased ones, can take on values 0, 1, 2, 3 (there are 6 - 3 = 3 non-defective computers).

The sample space:

$S = \begin{Bmatrix} NNN, NND, NDN, NDD, DNN, DND, DDN, DDD\end{Bmatrix}.$

With each sample point we'll associate a value of the random variable X:

$NNN\qquad X=0\\NND\qquad X=1\\NDN\qquad X=1\\NDD\qquad X=2\\$

$DNN\qquad X=1\\DND\qquad X=2\\DDN\qquad X=2\\DDD\qquad X=3\\$