Mean or Expected Value and Standard Deviation · Exercise 25

A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 10% chance of returning $5,000,000 profit, a 30% chance of returning $1,000,000 profit, and a 60% chance of losing the million dollars. The second company, a hardware company, has a 20% chance of returning $3,000,000 profit, a 40% chance of returning $1,000,000 profit, and a 40% chance of losing the million dollars. The third company, a biotech firm, has a 10% chance of returning $6,000,000 profit, a 70% of no profit or loss, and a 20% chance of losing the million dollars.

(a) Construct a PDF for each investment.
(b) Find the expected value for each investment.
(c) Which is the safest investment? Why do you think so?
(d) Which is the riskiest investment? Why do you think so?
(e) Which investment has the highest expected return, on average?

OpenStax, Introductory Statistics 2e · §4.2 Mean or Expected Value and Standard Deviation · Exercise 25