EX 3.9 laptop or desktop

Consider whether the next person buying a computer at a certain electronics store buys

• a laptop
• or a desktop model. Let $X=\{\begin{array}{ll}1& \text{ if the customer purchases a desktop computer }\\ 0& \text{ if the customer purchases a laptop computer }\end{array}$ If $20\%$ of all purchasers during that week select a desktop, the pmf for $X$ is

$$\begin{array}{rl}p(0)& =P(X=0)=P\text{(next customer purchases a laptop model)}=0.8\\ p(1)& =P(X=1)=P\text{(next customer purchases a desktop model)}=0.2\\ p(x)& =P(X=x)=0\text{for}x\ne 0\text{or}1\end{array}$$

An equivalent description is $p\left(x\right)=\{\begin{array}{ll}.8& \text{ if }x=0\\ .2& \text{ if }x=1\\ 0& \text{ if }x\ne 0\text{ or }1\end{array}$

Figure 3.2 is a picture of this pmf, called a line graph.

• $X$ is, of course, a Bernoulli rv
• $p\left(x\right)$ is a Bernoulli pmf.

Figure 3.2 The line graph for the pmf in Example 3.9