Referring to the OP and writing from a smidgen of mathematics knowledge:
In here, talking about random, usually means a private key, 256 random bits.  Now think of them as a pattern.  a 256 bit long pattern.

Some, even many, patterns can be proven to not be random.  For example, if the bits make up the ASCII sequence "this is random" it definitely is not random.
But, it is almost impossible to prove randomness.  There may always be one more way to look at the number to find it not random.

So: As has been said, you must understand the hardware and software used to produce the number.  A difficult task.  Many have written words to the effect:  Don't try to generate a random number on your own.  It is extremely difficult.  When your number is not random, you won't know it until your coins are gone.