9. Partial Differential Equations

Try these first

1. 1.

   Find the expectation of the number of heads in three tosses of a fair coin.

   Hint

   Use the probabilities of getting heads for 0, 1, 2, and 3 heads.

2. 2.

   If X represents the outcome of rolling a fair six-sided die, calculate E(X).

   Hint

   Sum the outcomes weighted by their probabilities.

3. 3.

   What is the expected value of a discrete random variable?

   • The maximum possible outcome
   • The average of all outcomes
   • The product of outcomes

   Hint

   Think about how it gives a central tendency of the outcomes.

4. 4.

   True or False: The expectation of a constant is equal to the constant itself.

   • True
   • False

   Hint

   Consider what happens when you roll a die with the same number every time.

5. 5.

   Consider a random variable Y that can take values 1, 2, or 3 with probabilities 0.2, 0.5, and 0.3 respectively. Calculate E(Y).

   Hint

   Use the weighted average formula for discrete random variables.

6. 6.

   A uniform distribution ranges from -1 to 1. Determine the expected value of this distribution.

   Hint

   Recall how the midpoint formula gives you the average.