Q:

Is the random function not computable? 

Some days ago I read about the Church-Turing Thesis and it establishes that any function can be described as an algorithm, so being defined as computable, and no function mismatches the Thesis.  But, what about random function?  If our computers are Turing Machines, and pure randomness cannot be obtained in a computer, is the random function non computable? 

A:

One of the properties that a function has is that it gives a unique output when given a particular input.   The random "function" does not possess this property, and hence the Church-Turing Thesis does not apply to it.