Answer to Question #186969 in Statistics and Probability for Anthonette parco

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: