The Hardest Interview 2 |top| ✪

[ 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)).

where (b', g') are updated after one more child, assuming (p_n) based on their estimate (\hatR). the hardest interview 2

Set (\Delta U = 0) → threshold (p_\textthresh = 2\lambda). [ R_n = \fracB_nG_n,\quad B_n = B_n-1 +

where (k > 0) is a sensitivity parameter (here, (k=2)). [ R_n = \fracB_nG_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 ]

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

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