9.1.1. What is Expectation (Mean)?

Try these first

1. 1.

   What is the expected value of a single toss of a fair coin?

   Hint

   Consider the values head and tails represent.

2. 2.

   For a die roll with outcomes from 1 to 6, what is E(X)?

   Hint

   Use the average of all die outcomes.

3. 3.

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

   • 2
   • 3.5
   • 4

   Hint

   Think about how often each number occurs.

4. 4.

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

   • True
   • False

   Hint

   Consider what happens if the random variable was always that constant.

5. 5.

   In a city, the probability distribution of daily rainfall events can be described by a discrete random variable. If E(X) = 2 inches, how do you interpret this in practical terms?

   Hint

   Think about how this relates to planning activities.

6. 6.

   For a random variable X with a uniform distribution from 1 to 5, find the variance and relate it to the mean.

   Hint

   Use the variance formula for uniform distributions.