- **Calculus & Beyond Homework**
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- - **Determining Limiting Distribution**
(*http://www.physicsforums.com/showthread.php?t=347041*)

Determining Limiting Distribution1. The problem statement, all variables and given/known dataLet Xn have a gamma distribution with parameters alpha = n, and beta, where beta is not a function of n. Let Yn = Xn/n. Find the limiting distribution of Yn. 2. Relevant equations3. The attempt at a solution[tex]E(e^{tY_n}) = E(e^{t\frac{X_n}{n}})[/tex] I'm stuck here. I know that the MGF of a gamma distribution (in this case) is [tex](1-\beta t)^{-n}[/tex] I'm not sure with what to do about the 1/n in the MGF. Would it be just [tex]\frac{(1-\beta t)^{-n}}{n}[/tex] Any help would be appreciated. |

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