I did go through Korth's book of DBMS and I got these definitions:Uniformity:Each bucket is assigned the same number of search-key values from the set of all possible values.Randomness:Each bucket will have the same number of records assigned to it irrespective of the actual distribution of search-key values in the file.These definitions seem  similar to me. Can anyone please differentiate, I did search on net but can't understand.
Difference between properties of good hash function: uniformity and randomness
hashing