[問題] MGF問題
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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