Expected Values: Moments, Mode, Median, and Percentiles
Free SOA Exam P (Probability) lesson in Univariate Random Variables. 21 min read, ~3,088 words.
LOTUS: uses the distribution of, not, so stay in "X-land". Expected value: sum or integrate against the PMF/PDF, and it is linear:. Variance shortcut:, compute each piece separately. MGF:, with moments via. Median solves; mode maximizes or. Right-skewed distributions satisfy mean median mode; symmetric ones make all three coincide.
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What this lesson covers
- Content
- Example 1
- Example 2
- Example 3
- Example 4
- Common Mistakes
- Check Your Understanding
- Exam Shortcuts
Learning objectives
- 2c
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