Chapter 16, Problem 1E

(a)

To determine

To find: the expected value of every random variable.

Answer to Problem 1E

19

Explanation of Solution

Given:

$X$	10	20	30
$P\left(X=x\right)$	0.3	0.5	0.2

Formula used:

  $E\left(X\right)={\displaystyle \sum xP\left(x\right)}$

Calculation:

  $\begin{array}{c}E\left(X\right)={\displaystyle \sum xP\left(x\right)}\\ =10\left(0.3\right)+20\left(0.5\right)+30\left(0.2\right)\\ =3+10+6\\ =19\end{array}$

Expected value is 19.

(b)

To determine

To find: the expected value of every random variable.

Answer to Problem 1E

4.2

Explanation of Solution

Given:

$X$	2	4	6	8
$P\left(X=x\right)$	0.3	0.4	0.2	0.1

Formula used:

  $E\left(X\right)={\displaystyle \sum xP\left(x\right)}$

Calculation:

  $\begin{array}{c}E\left(X\right)={\displaystyle \sum xP\left(x\right)}\\ =2\left(0.3\right)+4\left(0.4\right)+6\left(0.2\right)+8\left(0.1\right)\\ =0.6+1.6+1.2+0.8\\ =4.2\end{array}$

Expected value is 4.2.