Do Statistical Laws Solve the 'Problem of Provisos'?

Earman and Roberts propose to interpret non-strict special science generalizations as statistical generalizations about correlations. Earman and Roberts claim that these statistical generalizations are not qualified by ceteris paribus (henceforth, cp) conditions. I present two challenges to the statistical account. According to the first challenge, the statistical account does not get rid of so-called "non-lazy" cp-conditions. This result undermines one of the alleged advantages of the statistical account. The second challenge is that the statistical account, qua general theory of special science laws, is weakened by the fact that idealized law statements resist a purely statistical interpretation