Chapter 13.4, Problem 24HP

To determine

To explain:

Experiment in which the expected value is not a possible outcome.

Answer to Problem 24HP

Rolling a die is an example of an experiment where the expected values are not a possible outcome.

Explanation of Solution

Rolling a de is an example of an experiment where the expected value is not a possible outcome.

Rolling a die has six possible outcomes $\left\{1,2,3,4,5,6\right\}$ .

Let $X$ represents the outcome of rolling a die. To find he expected value of $X$ using the equation,

  $E\left(X\right)={\displaystyle \sum _{x=1}^{6}xP\left(x\right)}$ where each probability of $X$ is equal to $\frac{1}{6}$

  $\begin{array}{l}E\left(X\right)={\displaystyle \sum _{x=1}^{6}xP\left(x\right)}\\ E\left(X\right)=1\left(\begin{array}{l}1\\ 6\end{array}\right)+2\left(\begin{array}{l}1\\ 6\end{array}\right)+3\left(\begin{array}{l}1\\ 6\end{array}\right)+4\left(\begin{array}{l}1\\ 6\end{array}\right)+5\left(\begin{array}{l}1\\ 6\end{array}\right)+6\left(\begin{array}{l}1\\ 6\end{array}\right)\\ E\left(X\right)=\frac{21}{6}\\ E\left(X\right)=3.5\end{array}$

Therefore, since the expected value of $3.5$ is not a possible outcomes for rolling a die. Rolling a die is an example of an experiment where the expected values are not a possible outcome.