A firm is considering two projects,A and B,with the following probability distributions for profit. $$\begin{array} { c c c }
\begin{array} { c }
\text { Prafit } \
\text { (\$1,000s) }
\end{array} & \begin{array} { c }
\text { Praject } A \
\text { Prabability } ( \% )
\end{array} & \begin{array} { c }
\text { Project } B \
\text { Prabability } ( \% )
\end{array} \
\hline \$ 20 & 10 & 10 \
40 & 15 & 15 \
60 & 50 & 25 \
80 & 15 & 40 \
100 & 10 & 10
\end{array}$$ Given the above,the variance of project A is
A)7.07
B)50
C)440
D)4,000
E)380

Question

A firm is considering two projects,A and B,with the following probability distributions for profit. $$\begin{array} { c c c } 
\begin{array} { c } 
\text { Prafit } \
\text { (\$1,000s) }
\end{array} & \begin{array} { c } 
\text { Praject } A \
\text { Prabability } ( \% )
\end{array} & \begin{array} { c } 
\text { Project } B \
\text { Prabability } ( \% )
\end{array} \
\hline \$ 20 & 10 & 10 \
40 & 15 & 15 \
60 & 50 & 25 \
80 & 15 & 40 \
100 & 10 & 10
\end{array}$$ Given the above,the variance of project A is
A)7.07
B)50
C)440
D)4,000
E)380

Quizplus · Accepted Answer

To calculate the variance of Project A, first, find the expected profit (mean), then use it to calculate the variance. The expected profit for Project A is calculated as follows: $$E(A) = (20 \times 0.1) + (40 \times 0.15) + (60 \times 0.5) + (80 \times 0.15) + (100 \times 0.1) = 2 + 6 + 30 + 12 + 10 = 60$$ Then, calculate the variance: $$Var(A) = [(20-60)^2 \times 0.1] + [(40-60)^2 \times 0.15] + [(60-60)^2 \times 0.5] + [(80-60)^2 \times 0.15] + [(100-60)^2 \times 0.1]$$ $$Var(A) = [1600 \times 0.1] + [400 \times 0.15] + [0 \times 0.5] + [400 \times 0.15] + [1600 \times 0.1]$$ $$Var(A) = 160 + 60 + 0 + 60 + 160 = 440$$

A Firm Is Considering Two Projects,A and B,with the Following