The Hardest Interview 2 | RECOMMENDED × 2027 |

[ U = \frac\text# boys\text# girls - \lambda \cdot \text(total births) ]

This creates negative feedback: If boys exceed girls nationally, (p_n < 0.5), and vice versa. At each step, before having another child, the family estimates current national ratio (\hatR) using: the hardest interview 2

Given uniform prior (\lambda \sim U[0.05,0.15]), after seeing (m) other families’ early stops, they update via Bayes. The problem becomes a with incomplete information. 6. Key Result (Numerical Simulation Summary) Monte Carlo simulations with (N=10^5) families, 1000 days, yield: [ U = \frac\text# boys\text# girls - \lambda

If (\Delta U < 0), they stop even if formal stopping rule not met (early stop). [ U_\texttotal = \sum_\textfamilies \left( \fracb_fg_f - \lambda \cdot t_f \right) ] They compute expected marginal utility of an additional

[ R_n \approx R_n-1 \cdot \frac1 + \fracp_nR_n-1 \cdot (1-p_n) \cdot G_n-1/B_n-11 + \frac1-p_nG_n-1 ]

where (b', g') are updated after one more child, assuming (p_n) based on their estimate (\hatR).

They compute expected marginal utility of an additional child: