Looking at the DC behavior of the almlifier and following the convention that lower case letters represent changes in the respective quantities:

The gain is

which for small r_E can be approximated by

Add bypass capacitor

Looking at the DC behavior of the almlifier and following the convention that lower case letters represent changes in the respective quantities:

The gain is

but for AC signal variations for which C_E is an effective bypass, the gain is

Remove bypass capacitor

With the bypass capacitor in place, the voltage gain is dertemined by the collector resistor R_C and the effective resistance of the transistor r_E.

This effective resistance is where RBE is the forward resistance of the base-emitter diode. Remove bypass capacitor