Originally posted by AThousandYoungThey was a drive to have more male babies in china and it certainly worked because a lot of female babies were killed at birth. Of course it came back to bite them in the asss 20 years later with a large excess of males and no females for them so they pretty much rioted so if such a drive is successful there will be repercussions down the road.
This is an assumption we may or may not be able to make, depending on how the problem is intended.
Originally posted by wolfgang59An interesting follower to the original question:
Taken as a statistical problem the ratio of births is 50/50 so the law has no effect on the overall ratio (althought the birth rate will reduce to less than 2 per couple and hence the population will decrease)
If every woman give birth to so many as she is allowed to do, i.e. until the first baby girl is born - (We're agreed that in the long run, the same number of boys as girls are born) - how many babies will the women give birth to on average in the country, in the long run?
Originally posted by FabianFnas(Assuming the idealised case is that straightforward - and we're not worriying about potentially immortal mothers with hundreds of sons...)
An interesting follower to the original question:
If every woman give birth to so many as she is allowed to do, i.e. until the first baby girl is born - (We're agreed that in the long run, the same number of boys as girls are born) - how many babies will the women give birth to on average in the country, in the long run?
The expected number would be:
0.5 + 2(0.5)^2 + 3(0.5)^3 + ...
I believe SUM{i = 1 to infinity}(i.x^i) = x/(1 - x)^2
Which gives us....(drum roll)....
2.
Originally posted by FabianFnasScenario 1 in my second post to this thread 🙂
An interesting follower to the original question:
If every woman give birth to so many as she is allowed to do, i.e. until the first baby girl is born - (We're agreed that in the long run, the same number of boys as girls are born) - how many babies will the women give birth to on average in the country, in the long run?
1 child with chance 1/2
2 children with chance 1/4
3 with chance 1/8
4 with chance 1/16
...
Gives a total of
1/2 + 1/4 + 1/8 + 1/16 + ...
+ 1/4 + 1/8 + 1/16 + 1/32 +...
+ 1/8 + 1/16 + 1/32 + ...
...
Which is
1
+ 1/2
+ 1/4
...
Which is 2.
I was thinking there ought to be an "inituitive" way of reaching that answer, rather than calculating infinite series. Here it is:
In this scenario, all families will, eventually, have one girl. Therefore, quite clearly, the average number of girls per family is one.
But we've already realised the proportion of boys to girls is still 50-50. So it must be true that the average number of boys per family is also one.
So the average family size = 1 + 1 = 2.
Originally posted by TheMaster37So the law of the emperor doesn't change the ratio beween boys and girls, not even in the long run.
Which is 2.
Originally posted by mtthw
So the average family size = 1 + 1 = 2.
And the nativity of 2 per woman isn't worse than many of the western countries.
Clever emperor...
Originally posted by mtthwVery nice.
I was thinking there ought to be an "inituitive" way of reaching that answer, rather than calculating infinite series. Here it is:
In this scenario, all families will, eventually, have one girl. Therefore, quite clearly, the average number of girls per family is one.
But we've already realised the proportion of boys to girls is still 50-50. So it must ...[text shortened]... the average number of boys per family is also one.
So the average family size = 1 + 1 = 2.
Originally posted by mtthwThe ONLY way to get the average figure of 2 is IF we have immortal women with hundreds of sons. Otherwise the average is less than two and the population declines as I said earlier.
(Assuming the idealised case is that straightforward - and we're not worriying about potentially immortal mothers with hundreds of sons...)
The expected number would be:
0.5 + 2(0.5)^2 + 3(0.5)^3 + ...
I believe SUM{i = 1 to infinity}(i.x^i) = x/(1 - x)^2
Which gives us....(drum roll)....
[b]2.[/b]
For instance lets limit the women to 8 sons.
Then we have 1 + 1/2 + 1/4 + ..... + 1/128 = 1 127/128
=approx 1.99 children per couple
Every birth is an independent event with the same odds of boy births, so this law won't have any significant effect.
I thought families which only ever have boys might raise the boy-to-girl ratio a little, but it ends up it doesn't.
Assumptions:
* 50% of births will be boys.
* All families obey the law.
* No baby girl gets killed purposefully. (I know, not realistic..)
* Families will continue to have children until they cannot, or they have 5 children.
Out of 32 families I arrive at the following numbers.
1 girl, 0 boys - 16 families
1 girl, 1 boy - 8 families
1 girl, 2 boys - 4 families
1 girl, 3 boys - 2 families
1 girl, 4 boys - 1 family
5 boys - 1 familiy
Girls - 16 + 8 + 4 + 2 + 1 = 31
Boys - 8x1 + 4x2 + 2x3 + 1x4 + 1x5 = 8 + 8 + 6 + 4 + 5 = 31
The point has been made above though, that this law will likely be effective for one reason... While half the conceptions will still be girls, many, many more of them will die before they are born (or just afterwards), because prospective parents will want to have more children and will thus sacrifice their girls to prevent being forbidden to have more children.
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Assuming each family continues having children until forbidden, then each sequence will end in a girl, therefore we have:
G (1/2)
BG (1/4)
BBG (1/8)
BBBG (1/16)
total girls = 1/2 + 1/4 + 1/8 + 1/16 + ... = sum(n=1..infinity) of 1/2^n
total boys = 1/4 + 2/8 + 3/16 + 4/32 + ... = sum(n=1..infinity) of n/2^(n+1)
which works out as total_boys = 1
So the ratio of boys to girls remains 1 to 1!