Expected Value and Variance

A.  $9.81 million.

B.  $12.20 million.

C.  $32.40 million.

[Solutions] B

expected sales is 0.05 × $70 + 0.70 × $40 + 0.25 × $25 = $3.50 million + $28.00 million + $6.25 million = $37.75 million.

The variance of sales: σ² (Sales) = P($70)[$70 – E(Sales)]² + P($40)[$40 – E(Sales)]² + P($25)[$25 – E(Sales)]² = 0.05($70 – 37.75)² + 0.70($40 – 37.75)² + 0.25($25 – 37.75)² = $96.18 million. The standard deviation is thus σ = ($96.18)^1/2 = $9.81 million.

The amount of the expected recovery is closest to:

A $36,400.

B $63,600.

C $81,600.

[Solutions] B

If Scenario 1 occurs, the expected recovery is 60%($50,000) + 40%($30,000) = $42,000, and if Scenario 2 occurs, the expected recovery is 90%($80,000) + 10%($60,000) = $78,000. Weighting by the probability of each scenario, the expected recovery is 40%($42,000) + 60%($78,000) = $63,600.