9.1.2. Expectation for Discrete Random Variables

Try these first

1. 1.

   What is the expectation of a fair coin toss?

   Hint

   Consider the probabilities of each outcome.

2. 2.

   Calculate the expectation for rolling a 4-sided die.

   Hint

   Add all outcomes and divide by the number of sides.

3. 3.

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

   • 2.5
   • 3
   • 3.5
   • 4

   Hint

   Think about the average of all the outcomes.

4. 4.

   Is the expected value of a constant equal to the constant itself?

   • True
   • False

   Hint

   Remember what a constant is.

5. 5.

   You roll two 6-sided dice. What is the expected value of the sum of the two rolls?

   Hint

   Calculate each die's expectation and sum them.

6. 6.

   Consider a random variable Z that can take values 0, 1, 2, or 3 with probabilities 0.1, 0.2, 0.4, and 0.3 respectively. Calculate E(Z) and variance.

   Hint

   Use the definition of expectation and then apply the variance formula.