It will of course hinge on some empiricism, like the heritability of IQ. You can either take some reasonable number based on the literature or have it be an unknown in your formula/simulation. You can assume the environment I will raise them in will be the average environment for some reasonable population.
Something something order statistic of bivariate normal distribution probably doesn't have a nice closed form solution so you'll have to estimate it, which should be quite easy.
A valid submission will include: a mathematical function or code function to calculate the number of children to get a probability of at least 'p' that at least one of the children will have IQ at least 'A'.
The function parameters should be:
A and B: me and my partner's IQ
H: the heritability of IQ
p: the target probability.
You also need to calculate the number for these specific values:
A=140
B=130
H=0.6
p=0.9
Market resolves YES if someone posts a valid submission in the comments by market close, otherwise resolves NO.
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This seems correct if the assumptions are correct (in particular the meaning of heritability): https://chat.openai.com/share/897f35b9-8e9c-4ab5-be2b-dfcc80a12534
@mariopasquato Yep, there is a mistake. If H is 1 the result is even smaller (n=5), which cannot be right. The correct version has std_dev_IQ = math.sqrt(15**2 *(1-H) ). But the answer to the question finally depends on the opinion of the author on the disclaimer ChatGPT sagely included at the end.
@SorinTanaseNicola At any rate your answer below should probably be enough for resolution, right? @levifinkelstein good luck raising 7 kids
If the standard deviation of IQ is 15, then non-genetic factors should account for approximately 9.5 points, representing a 40% variation. Consequently, there is about a 30% chance that a child will have an IQ more than 5 points above the average IQ of the parents. Therefore, seven children should be sufficient. Considering the quality and quantity of available data, I am convinced that no quantitative analysis would yield significantly better results than this. Therefore, I suggest carefully selecting the mothers...