Final answer:
To calculate the expected return, multiply each outcome by its probability and sum them up. The investment with the highest expected return, on average, is the hardware company with $600,000. To calculate the variance, calculate the squared difference between each outcome and the expected return, multiply it by its probability, and sum them up.
Step-by-step explanation:
To calculate the expected return, you multiply each possible outcome by its corresponding probability and sum them up. Let's calculate the expected return for each investment:
The expected return for the first investment, the software company, is (0.10 * $5,000,000) + (0.30 * $1,000,000) + (0.60 * -$1,000,000) = $200,000.
The expected return for the second investment, the hardware company, is (0.20 * $3,000,000) + (0.40 * $1,000,000) + (0.40 * -$1,000,000) = $600,000.
The expected return for the third investment, the biotech firm, is (0.10 * $6,000,000) + (0.70 * $0) + (0.20 * -$1,000,000) = $500,000.
To calculate the variance, you need to calculate the squared difference between each outcome and the expected return, multiply it by its probability, and sum them up. The formula for variance is too complex to include here, but you can calculate it using a calculator or computer software.