Okay. I see
If I use the bersion without the PCB i need the resustance, because the signal float.
I thought i can do it without the resistance and calculate the value correct
The 3 pin version is the same 4 pin sensor, except it is mounted to a PCB that provides the 10K pullup resistor for the signal pin to ensure it is pulled up to High by default. If you are using the same 4 pin sensor which is not mounted on the PCB board then yes you need the 10K resistor, otherwise the signal pin may potentially float.
On what you posted the Data line needs a 10K pullup resistor between Data and Vcc. Using some off the shelf boards include the pullup and some don't. On the DHT11 and DHT22 modules only 3 pins are used exactly as shown in your image. Pin 3 is clearly labeled N/C (No Connection) which is why the board only has 3 pins.