### Solutions to Risk Measurement Problems

 Problem 1 Outcome Probability Outcome value px x-E(x) (x-E(x))2 p(x-E(x))2 Pessimistic 10% \$1,000,000 \$100,000 -\$3,700,000 13,690,000,000,000 1,369,000,000,000 Moderate 40% \$4,000,000 \$1,600,000 -\$700,000 490,000,000,000 196,000,000,000 Optimistic 50% \$6,000,000 \$3,000,000 \$1,300,000 1,690,000,000,000 845,000,000,000 100% E(x) = \$4,700,000 variance = 2,410,000,000,000 s = \$1,552,417 Problem 2 Outcome Probability Outcome value px x-E(x) (x-E(x))2 p(x-E(x))2 One 10% 60% 0.060000 0.320000 0.102400 0.010240 Two 50% 40% 0.200000 0.120000 0.014400 0.007200 Three 30% 20% 0.060000 -0.080000 0.006400 0.001920 Four 10% -40% -0.040000 -0.680000 0.462400 0.046240 E(x) = 0.280000 variance = 0.065600 s = 25.61% Problem 3 Outcome Probability Outcome value px x-E(x) (x-E(x))2 p(x-E(x))2 A 10% \$1,000 \$100 -\$2,000 4,000,000 400,000 B 20% \$2,000 \$400 -\$1,000 1,000,000 200,000 C 40% \$3,000 \$1,200 \$0 0 0 D 20% \$4,000 \$800 \$1,000 1,000,000 200,000 E 10% \$5,000 \$500 \$2,000 4,000,000 400,000 E(x) = \$3,000 variance = 1,200,000 s = \$1,095