Raw Ground Beef and any other raw meat including Poultry is safe in the fridge for 2 days.
After 2 days the Ground Beef and other meats go bad and should be thrown out.
If you want to keep the Ground Beef longer than 2 days then you should freeze it instead since the Raw Ground Beef can keep for up to 4 months in the freezer.
The Ground Beef will still be safe even if it does turn brown as long as it's been frozen.