Interview 2 !new! — The Hardest

Additionally, the government secretly measures not the raw gender ratio, but a :

[ \Delta U = \mathbbE\left[ \fracb'g' - \fracbg \right] - \lambda \cdot 1 ] the hardest interview 2

[ p_n = \frac11 + e^-k \cdot (R_n-1 - 1) ] Additionally, the government secretly measures not the raw

For large (N) families, this is approximately deterministic: yield: [ R_n = \fracB_nG_n

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:

[ R_n = \fracB_nG_n,\quad B_n = B_n-1 + X_n,\ G_n = G_n-1 + (1-X_n) ] where (X_n \sim \textBernoulli(p_n)).

| (\lambda) | Final national (E[b/g]) | Avg. children per family | Avg. utility per family | |-------------|----------------------------|--------------------------|--------------------------| | 0.05 | 1.023 | 2.91 | 0.955 | | 0.10 | 1.007 | 2.68 | 0.891 | | 0.15 | 0.994 | 2.44 | 0.847 |