EX 3.26 (EX 3.23 continued)

(Continue EX 3.23 repurchase unsold computer) In the computer sales scenario of Example 3.23, $E\left(X\right)=2$ and $E\left(X^2\right)={\left(0\right)}^2\left(.1\right)+{\left(1\right)}^2\left(.2\right)+{\left(2\right)}^2\left(.3\right)+{\left(3\right)}^2\left(.4\right)=5$ so $V\left(X\right)=5-{\left(2\right)}^2=1.$

The profit function $h\left(X\right)=800X-900$ then has variance ${\left(800\right)}^2\cdot V\left(X\right)=\left(640,000\right)\left(1\right)=640,000$ and standard deviation 800 .