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