During Beta decay experiments it was found that momentum and energy were not conserved as they should be. In Beta decay, a Neutron from the nucleus decays into a Proton and a high speed Electron (beta particle).
Or more generally we can just consider the Neutron decaying to form a Proton and an Electron.
This decay should give an Electron of known Kinetic Energy, however, experimentally this is not the case:-
Pauli explained the range of energies by suggesting that another particle was also being emitted, sharing the Kinetic Energy.
In order to match experimental observations, the particle must:-
1. Have a very small mass
2. Have a neutral charge
3. Be highly penetrating
The particle became known as the Neutrino.
Therefore the formula should actually be written as:-
The video below gives a more detailed explanation of Beta decay for both and Electron and a Positron.