Regarding lesson 4 in the series on faith

 
Hello Rabbi Michi,
In lesson 4 of your series on faith (thanks again for the excellent series on YouTube), you deal with the difficulty of commanding a person to believe in a fact and how this fits in with Mitzvah A to the Rambam. You suggest that it may be that the command is indeed about examination and investigation and not about belief itself. According to this, there could be a person who in fact does not believe but nevertheless fulfills the mitzvah because he has investigated and tested, on the other hand, a person who in fact does believe but does not fulfill the mitzvah because his belief is not based on independent investigation and examination but on intuition or on trust in tradition and education, and so on. Is this true? Is it obligatory for a person who already believes in God, but not by virtue of examination and investigation, to go out and investigate in order to fulfill the mitzvah?