Moments for Linear Combinations of Independent Random Variables
Free SOA Exam P (Probability) lesson in Multivariate Random Variables. 20 min read, ~2,932 words.
Mean is linear (always):, no independence needed. Variance under independence:, coefficients SQUARED. Constants vanish from variance:. Negative coefficients stay positive:, so every variance contribution is non-negative. Sample mean: for iid; use when independent but not identical. Dependence adds covariance: when not independent, add to the variance. Second moment:. Convert distributions...
Read the full lesson, free →
Worked examples and practice. Free with a free account, no card.
What this lesson covers
- Content
- Example 1
- Example 2
- Example 3
- Common Mistakes
- Check Your Understanding
- Exam Shortcuts
Learning objectives
- 3h
Browse all free Exam P lessons or jump into free Exam P practice questions.