Final answer:
Douglas should recommend the investment with the higher expected value if both investments are equally risky. The expected value is calculated by weighing each outcome by its probability of occurrence. Safety and risk can be assessed by comparing the variances or standard deviations of the investments.
Step-by-step explanation:
To determine which investment Douglas should recommend, one would need to calculate the expected value for each investment. Expected value provides a weighted average of all possible outcomes, where each outcome is weighted according to its probability of occurrence, giving a measure of the central tendency of the random variable representing investment returns.
If Investment Y has a higher expected return than another investment, it would suggest that over time, Investment Y would yield more on average. The expected value is calculated by multiplying each possible outcome by its probability and summing all these values.
To assess the risk of each investment, one could examine the variance or standard deviation of the possible outcomes from their expected values. The investment with the lower variance would be considered the safest because it would have less volatility or variability in returns. Conversely, the investment with a higher variance is seen as riskier due to greater volatility.
Investment X might be considered the safest investment if it has the lowest variance, while Investment Y might be the riskiest investment if it has the highest variance. However, Investment Y might also provide the highest expected return despite being riskier.