I know that the inference pattern of double slit experiment is actually a result of the ensemble of particles hit the screen.

My problem is this.

If we close one slit at a time at a certain frequency, then the interference pattern is not 'wave-like'.

Then we close and open both slits at the same time with the same frequency as above. This time we will get a 'wave-like' interference.

We will consider large number of ensembles however I do not think we can obtain this difference by considering probabilities for statistical ensemble without thinking a probability of a quantum particle goes through a slit has a miraculous effect from the status of the distant slit.

Is there any way to solve this problem by statistical interpretation?

Does statistical interpretation embraces the fact that the distant slit affects probability? If so what is the difference from the Copenhagen interpretation?

(If this is a famous discussion, please provide a link or reference to how this is explained in statistical interpretation. That's sufficient.)