Expected Value Math Example 1

Solution

1. 1
   A fair die has six equally likely outcomes $\{1,2,3,4,5,6\}$, each with probability $\frac{1}{6}$.
2. 2
   Apply the expected value formula: $$E(X) = \sum x_i \cdot P(x_i) = \frac{1}{6}(1 + 2 + 3 + 4 + 5 + 6)$$
3. 3
   Compute the sum: $$\frac{1}{6} \times 21 = \frac{21}{6} = 3.5$$