When two random variables X and Y are independent:
E(X+Y) = E(X) + E(Y) (also true when they are not independent)
V(X+Y) = V(X) + V(Y) (only when independent)
Example ① Find the expected value of the sum of the numbers on two dice.
Solution:E(X₁+X₂) = 3.5 + 3.5 = 7
Solution:E(X₁+X₂) = 3.5 + 3.5 = 7
Key Point
- Expected values can always be added; variances can be added when independent
Practice Problems
- Find the variance of the sum of the numbers on two independent dice.
Solutions and Explanations
- Solution:35/6
2·35/12=35/6.