Hello,

So if you take the log, that'll give something like

But actually, the pmf of X is

Then the global pmf of the sample of n binomial distributions is

And then you have to take the log of this product.

But I feel like there'll be a problem for differentiating, since it's a discrete distribution... and googling for "discrete fisher information" didn't yield anything interesting. Maybe you know...

I hope that helps.