How to make function (when you know variables)?

[NAGG]

Hello.
The main question is in this picture.


I understand everything. One question:
How to get A(η) funtion using etas (we know function with mean and variance; I have to change it to η variables; In my case η1 and η2 )? I think it is very easy question how to do i, but I am stuck on this basic function problem.

Thank you for your help!

 

[Dr.Peterson]

I think you're asking how to get from the LHS to the RHS of

​

given that

​

All this means is solving the system of equations

[MATH]\eta_1=\frac{\mu}{\sigma^2}[/MATH]​

[MATH]\eta_2=\frac{-1}{2\sigma^2}[/MATH]​

Solve the second equation for \(\sigma\), then put that into the first. Then replace \(\mu\) and \(\sigma\) in the LHS.