Chapter 16, Problem 2E

(a)

To determine

To find: the expected value of every random variable.

Answer to Problem 2E

1.2

Explanation of Solution

Given:

$X$	0	1	2
$P\left(X=x\right)$	0.2	0.4	0.4

Formula used:

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

Calculation:

  $\begin{array}{c}E\left(X\right)={\displaystyle \sum xP\left(x\right)}\\ =0\left(0.2\right)+1\left(0.4\right)+2\left(0.4\right)\\ =0.4+0.8\\ =1.2\end{array}$

Expected value 1.2

(b)

To determine

To find: the expected value of every random variable.

Answer to Problem 2E

280

Explanation of Solution

Given:

$X$	100	200	300	400
$P\left(X=x\right)$	0.1	0.2	0.5	0.2

Formula used:

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

Calculation:

  $\begin{array}{c}E\left(X\right)={\displaystyle \sum xP\left(x\right)}\\ =100\left(0.1\right)+200\left(0.2\right)+300\left(0.5\right)+400\left(0.2\right)\\ =10+40+150+80\\ =280\end{array}$

Expected value is 280