Question

Determine the possible values and construct the probability distribution for the random variables described in each of the following situations. Draw the corresponding histogram for aech probabilty

2. A shipment of five computers contain two that are defective. If a reatailer receives three of these compiters at random, list the elements of the sample space S using the letters D and N for defective and non-defective computers, respectively. To each sample point assign a value x of the random variable x representing the number of computers purchased by the retailer which are defective.

Answer 1

Solution:

Given, N denotes the number of non-defective computers and D denotes defective.

$\begin{array}{l} \text { 3N, 0D: } \\ \begin{array}{l} \text { X=0 } \\ \text { P }(3 \mathrm{~N}, 0 \mathrm{D}) \end{array} \end{array}$

$=^3C_3\times(^2C_0/ ^5C_3)=1\times(1/10)=0.1$

$2 \mathrm{~N}, 1 \mathrm{D}:\\ \mathrm{X}=1\\ \mathbf{P}(2 \mathbf{N}, \mathbf{1} \mathbf{D})$

$=^3C_2\times(^2C_1/ ^5C_3)=3\times(2/10)=0.6$

$1 \mathrm{~N}, 2 \mathrm{D}:\\ \begin{array}{l}\\ \mathrm{X}=2 \\ \qquad \begin{array}{r} \\ \end{array} \end{array}$

$\mathrm{P}(\mathbf{1 N}, 2 \mathrm{D})=^3C_1\times(^2C_2/ ^5C_3)=3\times(1/10)=0.3$

Histogram: