I believe that you are intellectually mature to play this game, try convincing your mom about this though

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You can try explaining to her that violent video games dont necessarily make an already sane person violent and maybe gather some research info on this.
In the end, its just a game! Not real life! Besides violent-ish games like MW2 help you to let of some steam and relieve stress.
I had been playing much much more violent videogames when i was at your age. My parents would rarely look on what i was exactly playing on my pc and didnt seem to care at all. Someday my mum would ask me what games I like (btw she knows nothing about PCs and video games).I showed her some Half Life 1 gameplay and maybe some Call of Duty 2.Of course she thought that they were extremely violent but she
trusted me. My father, he would rarely be at home but sometimes he would stare at my pc screen as I was playing S.T.A.L.K.E.R and Half LIfe 2.He knows quite a bit about PCs but never played any games.After commenting on the game's realistic graphics and incredible atmosphere, he never mentioned anything about violence.
Now over 3 years have passed and im not violent at all (as a matter of fact i used to be more violent before i was playing video games).
FYI both my parents are psychologists, I dont think that it proves anything but they are not completely clueless about human's behaviour e.t.c.
Well i can only wish you good luck!