At max level the Professional Class Mod grants the following 2 stat bonuses:
Reload Speed: +58.5%
Shield Capacity: +1,053,349
Bug (Credit: Demonite)
Item Card displays false Reload Speed value.
Borderlands 2 Class Mods can boost up to 6 different skills by 4, 5 or 6 Points. A Class Mod's Bonus Point distribution depends on its rarity, level and parts.
Here are the maximum distributions at Level 50 and above:
Slayer of Terramorphous: (4/4/4/4/4)
The Skills an Armor comes with depend on the 2 Classes Powers and their order. Select the Main and Secondary Class to see the Armor's Prefix and which skills it can have.
Base Game - World Drop
Borderlands 2 World Drops are items that drop from any suitable Loot Source in addition to their dedicated sources.
There are 67 unique items in the World Drop pool, so for farming 1 of the 6 class mods it's best to seek out its dedicated Loot Source.
If you still want to test your luck, you should equip a Vault Hunter's Relic to indirectly increase your chance of a World Drop Legendary.
Suitable Loot Sources:
Loot Luck Formula
P = Dedicated Loot Pool Chance
L = Loot Luck