Let's say I have a blackbox function generate_number() that generates a random number between 1-N; and assume N is known.

I use this to generate X numbers; let's say these numbers are not stored anywhere so i can't build an exact list of them.

I also have another blackbox function num_seen_numbers() that tells me Y which is how many unique numbers of the N numbers have been generated.

For example. Let's say N = 100 (given), and I call generate_number() 40 times (X = 40). Then I call num_unseen_numbers() and it says out of the total N = 100 possible numbers, it has only generated 15 unique ones (Y = 15).

Is there a way to to determine the likelihood that generate_number() has an underlying uniform probability distribution for it's generation?

Let's say I have a blackbox function generate_number() that generates a random number between 1-N; and assume N is known. Each function call is independent from each other and carries no state.

I use this to generate X numbers; let's say these numbers are not stored anywhere so i can't build an exact list of them.

I also have another blackbox function num_seen_numbers() that tells me Y which is how many unique numbers of the N numbers have been generated.

For example. Let's say N = 100 (given), and I call generate_number() 40 times (X = 40). Then I call num_unseen_numbers() and it says out of the total N = 100 possible numbers, it has only generated 15 unique ones (Y = 15).

Is there a way to to determine the likelihood that generate_number() has an underlying uniform probability distribution for it's generation?