How to test a random generator

Question

I need to test a random number generator which produces numbers randomly. How to make sure the numbers generated are random.

Answer 1

How to make sure the numbers generated are random.

You can't make sure, there is no way to distinguish with certainty any function from a random number generator using a finite number of tests. But you can do Statistical Analysis:

So, if it is impossible to definitively prove randomness, what can we do instead? The pragmatic approach is to take many sequences of random numbers from a given generator and subject them to a battery of statistical tests. As the sequences pass more of the tests, the confidence in the randomness of the numbers increases and so does the confidence in the generator. However, because we expect some sequences to appear nonrandom (like the ten rolls of six on our die), we should expect some of the sequences to fail at least some of the tests. However, if many sequences fail the tests, we should be suspicious. This is also the way you would intuitively test a die to see if it is loaded: Roll it many times, and if you see too many sequences of the same value coming up, you should be suspicious.

See the section on Charmaine Kenny's study for more details on the tests you could run.