# Step-by-Step Solution Let's solve the problem step by step: ### **Given Data** | State of Economy | Probability (P) | Return (R) | |------------------|-----------------|------------| | Boom | 0.45 | 25% | | Normal | 0.50 | 15% | | Recession | 0.05 | 5% | --- ## **Step 1: Calculate Expected Return (\(\bar{R}\))** \[ \bar{R} = \sum [P_i \times R_i] \] \[ \bar{R} = (0.45 \times 0.25) + (0.50 \times 0.15) + (0.05 \times 0.05) \] \[ \bar{R} = 0.1125 + 0.075 + 0.0025 = 0.19 \] **Expected Return = 19%** --- ## **Step 2: Calculate Standard Deviation (\(\sigma\))** \[ \sigma = \sqrt{\sum [P_i \times (R_i - \bar{R})^2]} \] Calculate each squared deviation: - For Boom: \( (0.25 - 0.19)^2 = (0.06)^2 = 0.0036 \) - For Normal: \( (0.15 - 0.19)^2 = (-0.04)^2 = 0.0016 \) - For Recession: \( (0.05 - 0.19)^2 = (-0.14)^2 = 0.0196 \) Multiply by probabilities: - Boom: \(0.45 \times 0.0036 = 0.00162\) - Normal: \(0.50 \times 0.0016 = 0.0008\) - Recession: \(0.05 \times 0.0196 = 0.00098\) Sum: \[ 0.00162 + 0.0008 + 0.00098 = 0.0034 \] Take the square root: \[ \sigma = \sqrt{0.0034} \approx 0.0583 \] **Standard Deviation = 5.83%** --- ## **Step 3: Calculate Coefficient of Variation (CV)** \[ CV = \frac{\sigma}{\bar{R}} \] \[ CV = \frac{0.0583}{0.19} \approx 0.307 \] --- ## **Final Answers** - **Expected Return:** **19%** - **Standard Deviation:** **5.83%** - **Coefficient of Variation:** **0.307** (or **30.7%**) --- ### **Summary Table** | Statistic | Value | |------------------------|-------------| | Expected Return (\(\bar{R}\)) | 19% | | Standard Deviation (\(\sigma\)) | 5.83% | | Coefficient of Variation (CV) | 0.307 (30.7%) | --- If you need the answers rounded differently or in a different format, let me know!