1. **State the problem:** We need to calculate the expected rate of return and the coefficient of variation for Stock Y given its probability distribution and standard deviation. 2. **Given data:** - Probabilities: $0.1, 0.2, 0.4, 0.2, 0.1$ - Returns for Stock Y: $-35\%, 0\%, 20\%, 25\%, 45\%$ - Standard deviation for Stock Y: $20.35\%$ 3. **Formula for expected rate of return:** $$E(R) = \sum (p_i \times r_i)$$ where $p_i$ is the probability and $r_i$ is the return. 4. **Calculate expected return:** $$E(R_Y) = 0.1 \times (-35) + 0.2 \times 0 + 0.4 \times 20 + 0.2 \times 25 + 0.1 \times 45$$ $$= -3.5 + 0 + 8 + 5 + 4.5 = 14\%$$ 5. **Formula for coefficient of variation (CV):** $$CV = \frac{\text{Standard Deviation}}{E(R)}$$ 6. **Calculate CV for Stock Y:** $$CV_Y = \frac{20.35}{14} \approx 1.4536$$ 7. **Interpretation:** The expected return of Stock Y is $14\%$ and the coefficient of variation is approximately $1.45$, indicating the risk per unit of return. **Final answers:** - Expected rate of return for Stock Y: $14\%$ - Coefficient of variation for Stock Y: $1.45$