The expected value E(X) (also denoted μ or mean) of a random variable X is
E(X) = Σ x_i · p_i
Example ① Find the expected value of a die roll.
Solution:E(X) = (1+2+3+4+5+6)/6 = 21/6 = 3.5
Solution:E(X) = (1+2+3+4+5+6)/6 = 21/6 = 3.5
Key Point
- Expected value is the “average value”
- E(aX+b) = a·E(X) + b
Practice Problems
- If X=1,2,3 have probabilities 1/2, 1/3, 1/6, respectively, find E(X).
Solutions and Explanations
- Solution:5/3
1·1/2+2·1/3+3·1/6=1/2+2/3+1/2=5/3.