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The Hardest Interview 2 Patched Page

[ 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)).

[ 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 ] the hardest interview 2

[ p_n = \frac11 + e^-k \cdot (R_n-1 - 1) ] [ R_n = \fracB_nG_n,\quad B_n = B_n-1 +

| (\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 | Using Bayesian learning, after several days they form

[ \hatR = R_n-2 + \epsilon,\quad \epsilon \sim \mathcalN(0, \sigma^2),\ \sigma=0.03 ]

For large (N) families, this is approximately deterministic:

If (\lambda = 0.1), threshold (p=0.2). If estimated (p < 0.2), they stop early. Families observe historical stops and national ratio changes. Using Bayesian learning, after several days they form a posterior on (\lambda). This influences future stopping.