CFO Director

The financial director has determined the following profitability scenarios for a new branch of the company:

Profit of 5 million CZK with probability 0.1.
Profit of 3 million CZK with probability 0.3.
Profit of 1 million CZK with probability 0.4.
Loss of 2 million CZK with probability 0.2.

Determine the expected value and standard deviation of the new branch's revenues.

Final Answer:

m =  1.4 mil
σ =  2.1071 mil

Step-by-step explanation:

$m=\frac{5\cdot 0.1+3\cdot 0.3+1\cdot 0.4+(-2)\cdot 0.2}{0.1+0.3+0.4+0.2}=1.4\text{mil}$

$$\begin{gathered} r=\frac{(5-m{)}^2\cdot 0.1+(3-m{)}^2\cdot 0.3+(1-m{)}^2\cdot 0.4+((-2)-m{)}^2\cdot 0.2}{0.1+0.3+0.4+0.2}=\frac{(5-1.4{)}^2\cdot 0.1+(3-1.4{)}^2\cdot 0.3+(1-1.4{)}^2\cdot 0.4+((-2)-1.4{)}^2\cdot 0.2}{0.1+0.3+0.4+0.2}=\frac{111}{25}=4.44 \\ \sigma =\sqrt{r}=\sqrt{4.44}=2.1071\text{mil} \end{gathered}$$

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