This was covered recently elsewhere on here. The short answer is I think med schools and residencies rarely perform random drug tests. I'm sure some do, but I suspect most are targeted at suspected students or residents. Most trust their students and residents enough that they don't subject them to random tests.
The second thing I would say is that I certainly knew some med students who smoked a healthy dose of marijuana during med school. Whether they continued throughout residency and/or into practice, I can't say. I'm sure the OP is not the only one, in other words.
All that said, I can't say this behavior is without risks. As others have pointed out, marijuana is still considered a Schedule I drug by the DEA, meaning it's illegal to use federally and has no known medical use according to the DEA. Even though some states are increasingly taking a liberal view of the drug, at the federal level it is still as illegal as it was 20 years ago. As you progress through your training, a clean bill of health regarding drug use will be required for you to maintain hospital privileges, keep your DEA prescribing license--and probably your medical license, as well. That's a lot to put on the line.
If you're talking a significant amount of daily use and you're worried about getting caught, perhaps you should consider seeing a mental health professional to see if a prescribed (legal) anxiolytic might help you?