1. **State the problem:** Calculate the expected return and standard deviation of a population given the returns: 9.6%, -15.4%, 26.7%, -0.2%, 20.9%, 28.3%, -5.9%, 3.3%, 12.2%, 10.5%. 2. **Convert percentages to decimals:** $$0.096, -0.154, 0.267, -0.002, 0.209, 0.283, -0.059, 0.033, 0.122, 0.105$$ 3. **Calculate the Expected Return (mean) $\mu$:** $$\mu = \frac{1}{n} \sum_{i=1}^n x_i = \frac{0.096 - 0.154 + 0.267 - 0.002 + 0.209 + 0.283 - 0.059 + 0.033 + 0.122 + 0.105}{10}$$ Calculate sum: $$0.096 - 0.154 = -0.058$$ $$-0.058 + 0.267 = 0.209$$ $$0.209 - 0.002 = 0.207$$ $$0.207 + 0.209 = 0.416$$ $$0.416 + 0.283 = 0.699$$ $$0.699 - 0.059 = 0.640$$ $$0.640 + 0.033 = 0.673$$ $$0.673 + 0.122 = 0.795$$ $$0.795 + 0.105 = 0.900$$ So, $$\mu = \frac{0.900}{10} = 0.09$$ Expected return is $9.0\%$. 4. **Calculate the population variance $\sigma^2$:** $$\sigma^2 = \frac{1}{n} \sum_{i=1}^n (x_i - \mu)^2$$ Find each squared difference: $$(0.096 - 0.09)^2 = 0.000036$$ $$(-0.154 - 0.09)^2 = (-0.244)^2 = 0.059536$$ $$(0.267 - 0.09)^2 = 0.177^2 = 0.031329$$ $$(-0.002 - 0.09)^2 = (-0.092)^2 = 0.008464$$ $$(0.209 - 0.09)^2 = 0.119^2 = 0.014161$$ $$(0.283 - 0.09)^2 = 0.193^2 = 0.037249$$ $$(-0.059 - 0.09)^2 = (-0.149)^2 = 0.022201$$ $$(0.033 - 0.09)^2 = (-0.057)^2 = 0.003249$$ $$(0.122 - 0.09)^2 = 0.032^2 = 0.001024$$ $$(0.105 - 0.09)^2 = 0.015^2 = 0.000225$$ Sum of squared differences: $$0.000036 + 0.059536 + 0.031329 + 0.008464 + 0.014161 + 0.037249 + 0.022201 + 0.003249 + 0.001024 + 0.000225 = 0.177474$$ So, $$\sigma^2 = \frac{0.177474}{10} = 0.0177474$$ 5. **Calculate the Standard Deviation $\sigma$:** $$\sigma = \sqrt{0.0177474} \approx 0.1332$$ 6. **Conclusion:** The expected return is $9.0\%$ and the population standard deviation is approximately $13.32\%$.