Question: 1. Dice. What is the expected number of spots observed in rolling a carefully balanced die once?
2. Profit from a risky investment. Rotter Partners is planning a major investment. The amount of profit X is uncertain, but a probabilistic estimate gives the following distribution (in millions of dollars):
Profit: 1 1.5 2 3 10
Probability: 0.3 0.2 0.2 0.2 0.1
What is the expected value of the profit?