Both are correct and yet they are different.
It depends on how you write your density.
Some write the density as
and others write it as
Um about the mean being the product of the two parameters.. Well when i did maths stats we proved that the mean for gamma was:
But now in this other subject, I'm asked to show that the mean is
So which one is correct, since you said both of the densities should have the mean being the product of the two parameters?
You should find the mean for both as an exercise and to clarify your thoughts.