9.2. Summary

Try these first

1. 1.

   What is the expectation of tossing a fair coin twice?

   Hint

   Consider the probabilities of getting 0, 1, or 2 heads.

2. 2.

   Calculate the expectation for a discrete random variable with values {1, 2, 3} and probabilities {0.2, 0.5, 0.3}.

   Hint

   Use the formula E(X) = ∑x_i * p_i.

3. 3.

   What is the expectation of rolling a fair 6-sided die?

   • 3
   • 3.5
   • 4

   Hint

   Consider how you can calculate the average of the sides.

4. 4.

   True or False: Expectation can be calculated using both sums and integrals.

   • True
   • False

   Hint

   Recall the different approaches to calculate expectation.

5. 5.

   Given X is a normal random variable with mean = 10 and variance = 4, calculate E(X + 3).

   Hint

   Use the linearity property of expectation.

6. 6.

   Explain how expectation can simplify the analysis of a probability distribution in financial modeling.

   Hint

   Think about the implications of average outcomes in risk assessment.