Investors use probabilities to decide among several potential investments and calculate potential returns, or losses. An investor has the possibility to invest $2 million in three different schemes. The first one has a 15% chance of returning $6 million profit, a 45% chance of returning $1 million and a 40% chance of losing $2 million. The second opportunity has a 30% chance of returning $2 million profit, a 30% chance of returning $1.5 million profit, and a 40% chance of losing $2 million. The third scheme has a 5% chance of returning $5 million profit, a 60% of no profit or loss, and a 35% chance of losing $2 million.

a. Construct a probability distribution function for each investment.

b. Find the expected value for each investment.

c. Calculate the standard deviation of investment 1.

d. Compare the standard deviations of each investment.

e. Which investment is the safest?