Q:

Why is there no resistor in a christmas LED string light?

I bought a bunch of different LED string lights for Haloween and Christmas. All of them are arranged as 2 sets in parallel. They are either 50 or 100 LEDs.
I noticed that most of them have a molded resistor built into each parallel circuit (which I believe is to handle any left voltage and limit maximum current).
However a few of them (models) don't seem to have any resistors built anywhere into the circuit. These have 50 LEDs (arranged in 2 parallel circuits). For example this one: https://www.homedepot.com/p/Home-Accents-Holiday-24-ft-100-Light-Cool-White-LED-Dome-Light-String-TY-100LD-W/305026726
There doesn't appear to any resistor anywhere. Just 2 tiny fuses in the power socket and the rest at all LEDs.
Is it okay to have a LED string light running off 110v without any resistors?
A couple of these LEDs have stopped working (they are dead, while the rest connected to the same series circuit are very faintly dim) so I need to buy replacement LEDs, without any resistor would I just assume the each LED would be 110v/25 = 4.4V forward voltage LED? What would happen if I used a 3.2v LED?

A:

Each LED has it's own internal resistance.  
When you consider the typical tolerance on AC lines is < 10%, and the tolerance on LED internal resistance can be up to 50% about the rated forward voltage, how many LEDs do you need to survive a 10% voltage tolerance without resistors and not exceed its current rating?
Well that depends on what nominal current you choose and the statistical variation of internal resistance on all batches.  I know the variation can be extremely small (<1%) in a single batch.  So the prudent choice is to use that value for the maximum voltage tolerance.
Consider an LED with the transfer function of Vf=2.8 + If*Ri for If rated @ 20mA and Ri = 16 +/-50% worst case i.e.  Vf 2.96 to 3.28  or 3 to 3.3V.  or 3 (+0.3V/-0)  (Some are better and worse than this example)
Now consider;

120V/3.0V = 40 LEDs 
120V/3.3V = 36 LEDs 
The LED tolerance on 40 LEDs is 40 *0.3V = 12.3V
The 10% tolerance on 120V is 12V, so it meets the criteria.

Conclusion
the more parts in series, the greater tolerance to applied voltage.

