**I have this function y:**

$ f(y)=y⋅e^{(−y/β)}$

**I need to find the moment estimator of β . α is given with α=2**

**This is what I did:**

$ \bar{Y}=α/(α+β)=2/(2+β)=∑Yi/n$

**Solving that for β**

and I get:

$ β=n/∑Yi$

**The correct answer is** $ β=∑Yi/2n$

Any help or guidance is appreciated.