Question

As in the title, I would expect it to be a nan as well. Is this number special?

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Solution

This is clearly a bug in numpy.ramdom.binomial.

Is this number special?

I would guess this is the result of some calculation involving the raw representation of nan (which is represented as a specific "reserved" float value). (More on that)

The implementor probably forgot to check input for nan and included the raw representation of nan in the (C-level) calculation.

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