Moment Generating Functions
Free SOA Exam P (Probability) lesson in Univariate Random Variables. 12 min read, ~1,862 words.
MGF definition:, and it must exist in a neighborhood of. k-th moment:, differentiate k times then evaluate at zero. Variance shortcut:, faster than the raw definition. Uniqueness: if for all near 0, then and share the same distribution. Sum of independents:, MGFs multiply (not add). Linear transform:. Closure under convolution...
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What this lesson covers
- Content
- Example 1
- Example 2
- Common Mistakes
- Check Your Understanding
- Exam Shortcuts
Learning objectives
- 2a
- 2b
- 2c
- 2d
- 2e
- 2f
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