[問題] MGF問題

[Danielhsieh (阿光)]

題目：

X_1........X_n~iid exp(v)

問Xbar的distribution.

答案是給gamma(alpha=n,beta=v/n)

但我怎麼算都是gamma(alpha=n,beta=1/(vn))



我算的步驟

E[e^(t*Xbar)]=E[e^(t/n*sumXi)]

=E[e^(t/n)X_1]*E[e^(t/n)X_2]*..............*E[e^(t/n)X_n]

since E[e^(t/n)X_1]=v/(v-t/n)

then E[e^(t*Xbar)]= |     1      |^n
                    | ---------- |
                    |  1-t/(vn)  |


請問是哪裡錯了？

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