A Poisson distribution with a mean of 1.84 results in about 45% of children being first born. In fact, the best you can do with any distribution is 54%. For example, if there are 10k couples, then there will be 18.4k children born, at most 10k of which can be first born; and 10/18.4 = 54%.
In fact, the only thing that matters for the distribution (once you know the mean) is the number of childless families, since they could have had a first born but didn't.
I haven't been able to figure out where 74% comes from. Is there some way to sample on a per-family basis to come up with this?
In fact, the only thing that matters for the distribution (once you know the mean) is the number of childless families, since they could have had a first born but didn't.
I haven't been able to figure out where 74% comes from. Is there some way to sample on a per-family basis to come up with this?
edit: spelling