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moment generating function of the sum of independent random variables
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(Corollary)
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Let $X_i$ be independent random variables for
 , let each $X_i$ have moment generating function $M_{X_i} (t)$ , and let $X=\sum_{i=1}^n X_i$ . Then the moment generating function of $X$ is $$ M_X(t)=\prod_{i=1}^n M_{X_i}(t) $$
Proof. By definition,
Now, since each $X_i$ is independent of the others, this becomes
as required. 
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"moment generating function of the sum of independent random variables" is owned by me_and. [ full author list (2) ]
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Cross-references: moment generating function, random variables, independent
This is version 2 of moment generating function of the sum of independent random variables, born on 2007-06-20, modified 2007-06-23.
Object id is 9628, canonical name is MomentGeneratingFunctionOfTheSumOfIndepententRandomVariables.
Accessed 1478 times total.
Classification:
| AMS MSC: | 60E05 (Probability theory and stochastic processes :: Distribution theory :: Distributions: general theory) |
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Pending Errata and Addenda
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