The intuitive argument was, of course, that the expected number of sons under such circumstances is 1, and since the expected number of daughters equals the expected number of sons, the expected family size must be 2, correct? How can adding a bunch of fractions be preferred to this? On Fri, Nov 6, 2015 at 11:46 AM, Henry Baker <hbaker1@pipeline.com> wrote:
Yes, but what happens the next & succeeding generations ?
(Assuming 1:1 "traditional" marriages.)
At 11:42 AM 11/6/2015, James Propp wrote:
Has anyone in the pop math biz tackled the mathematical side of the news story about China's (now abandoned) one-child-per-family policy?
Specifically, many families adopted the family planning algorithm "Have kids till you have a son, then stop", which (under idealized assumptions) gives rise to families of average size exactly 2.
A non-mathematician friend of mine asked me at dinner last night why the expected size of a family that stops when the first son is born is 2. I began to give him an intuitive argument that doesn't involve calculation, but he ended up preferring the argument that shows that 1/2 + 2/4 + 3/8 + ... = 2 by way of summing the formulas 1/2 + 1/4 + 1/8 + ... = 1 1/4 + 1/8 + ... = 1/2 1/8 + ... = 1/4 ... to obtain 1/2 + 2/4 + 3/8 + ... = 1 + 1/2 + 1/4 + ... = 2
Is there a place where this is explained, and explained well?
Jim Propp
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