[awegio]

According to the internet what you wrote is the distribution of min(random(), random()), but the distribution of the product is different.

Product: https://math.stackexchange.com/questions/659254/product-dist...

Minimum: https://stats.stackexchange.com/questions/220/how-is-the-min...

I can't explain it either, but I also don't think there is a reason they should look the same.